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Equation:
Equation sin(x)=0
Equation (7a+1)-(6a+3)=5
Equation 1/9*x^2-x+2=0
Equation x^3/(x^2-x-1)=0
Express {x} in terms of y where:
11*x+15*y=-8
-2*x-11*y=-4
-2*x-15*y=-3
2*x+12*y=-7
Identical expressions
x+ seven /(seven -x)^ three = zero
x plus 7 divide by (7 minus x) cubed equally 0
x plus seven divide by (seven minus x) to the power of three equally zero
x+7/(7-x)3=0
x+7/7-x3=0
x+7/(7-x)³=0
x+7/(7-x) to the power of 3=0
x+7/7-x^3=0
x+7/(7-x)^3=O
x+7 divide by (7-x)^3=0
Similar expressions
x+7/(7+x)^3=0
x-7/(7-x)^3=0

x+7/(7-x)^3=0 equation

The teacher will be very surprised to see your correct solution 😉

The solution

You have entered [src]

       7        
x + -------- = 0
           3    
    (7 - x)

x + \frac{7}{\left(7 - x\right)^{3}} = 0

Simplify

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

                         _______________________________________________________________________________________________________________________________________________________                                                                                 
                        /             ______________________                                                                                                                                                                                                     
                       /             /             ________                                                                                                                                                                                                      
                      /   49        /    343   7*\/ 199857                   14                                                      343                                                                                                                         
                     /    -- - 2*3 /   - --- + ------------  + ----------------------------- + --------------------------------------------------------------------------------                                                                                  
                    /     2      \/       16       144                ______________________               ____________________________________________________________________              ____________________________________________________________________
                   /                                                 /             ________               /             ______________________                                              /             ______________________                                 
                  /                                                 /    343   7*\/ 199857               /             /             ________                                              /             /             ________                                  
                 /                                             3*3 /   - --- + ------------             /   49        /    343   7*\/ 199857                   14                         /   49        /    343   7*\/ 199857                   14              
                /                                                \/       16       144         4*      /    -- + 2*3 /   - --- + ------------  - -----------------------------           /    -- + 2*3 /   - --- + ------------  - ----------------------------- 
               /                                                                                      /     4      \/       16       144                ______________________          /     4      \/       16       144                ______________________ 
              /                                                                                      /                                                 /             ________          /                                                 /             ________  
             /                                                                                      /                                                 /    343   7*\/ 199857          /                                                 /    343   7*\/ 199857   
            /                                                                                      /                                             3*3 /   - --- + ------------        /                                             3*3 /   - --- + ------------  
     21   \/                                                                                     \/                                                \/       16       144           \/                                                \/       16       144       
x1 = -- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------
     4                                                                                      2                                                                                                                            2

x_{1} = - \frac{\sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + \frac{49}{2} + \frac{343}{4 \sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}}}{2} + \frac{21}{4}

                                                                                                              ___________________________________________________________________________________________________________________________________________________________
                                                                                                             /               ______________________                                                                                                                      
                                                                                                            /               /             ________                                                                                                                       
                                                                                                           /     49        /    343   7*\/ 199857                   14                                                       343                                         
                                                                                             I*           /    - -- + 2*3 /   - --- + ------------  - ----------------------------- + ---------------------------------------------------------------------------------- 
                    ______________________________________________________________________               /       2      \/       16       144                ______________________               ______________________________________________________________________ 
                   / |            ______________________                                |               /                                                   /             ________               / |            ______________________                                |  
                  /  |           /             ________                                 |              /                                                   /    343   7*\/ 199857               /  |           /             ________                                 |  
                 /   |49        /    343   7*\/ 199857                   14             |             /                                               3*3 /   - --- + ------------             /   |49        /    343   7*\/ 199857                   14             |  
                /    |-- + 2*3 /   - --- + ------------  - -----------------------------|            /                                                  \/       16       144         4*      /    |-- + 2*3 /   - --- + ------------  - -----------------------------|  
               /     |4      \/       16       144                ______________________|           /                                                                                        /     |4      \/       16       144                ______________________|  
              /      |                                           /             ________ |          /                                                                                        /      |                                           /             ________ |  
             /       |                                          /    343   7*\/ 199857  |         /                                                                                        /       |                                          /    343   7*\/ 199857  |  
            /        |                                     3*3 /   - --- + ------------ |        /                                                                                        /        |                                     3*3 /   - --- + ------------ |  
     21   \/         |                                       \/       16       144      |      \/                                                                                       \/         |                                       \/       16       144      |  
x2 = -- + -------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
     4                                           2                                                                                                                                2

x_{2} = \frac{\sqrt{\left|{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}\right|}}{2} + \frac{21}{4} - \frac{i \sqrt{- \frac{49}{2} - \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{343}{4 \sqrt{\left|{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}\right|}}}}{2}

                                                                                                              ___________________________________________________________________________________________________________________________________________________________
                                                                                                             /               ______________________                                                                                                                      
                                                                                                            /               /             ________                                                                                                                       
                                                                                                           /     49        /    343   7*\/ 199857                   14                                                       343                                         
                                                                                             I*           /    - -- + 2*3 /   - --- + ------------  - ----------------------------- + ---------------------------------------------------------------------------------- 
                    ______________________________________________________________________               /       2      \/       16       144                ______________________               ______________________________________________________________________ 
                   / |            ______________________                                |               /                                                   /             ________               / |            ______________________                                |  
                  /  |           /             ________                                 |              /                                                   /    343   7*\/ 199857               /  |           /             ________                                 |  
                 /   |49        /    343   7*\/ 199857                   14             |             /                                               3*3 /   - --- + ------------             /   |49        /    343   7*\/ 199857                   14             |  
                /    |-- + 2*3 /   - --- + ------------  - -----------------------------|            /                                                  \/       16       144         4*      /    |-- + 2*3 /   - --- + ------------  - -----------------------------|  
               /     |4      \/       16       144                ______________________|           /                                                                                        /     |4      \/       16       144                ______________________|  
              /      |                                           /             ________ |          /                                                                                        /      |                                           /             ________ |  
             /       |                                          /    343   7*\/ 199857  |         /                                                                                        /       |                                          /    343   7*\/ 199857  |  
            /        |                                     3*3 /   - --- + ------------ |        /                                                                                        /        |                                     3*3 /   - --- + ------------ |  
     21   \/         |                                       \/       16       144      |      \/                                                                                       \/         |                                       \/       16       144      |  
x3 = -- + -------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
     4                                           2                                                                                                                                2

x_{3} = \frac{\sqrt{\left|{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}\right|}}{2} + \frac{21}{4} + \frac{i \sqrt{- \frac{49}{2} - \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{343}{4 \sqrt{\left|{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}\right|}}}}{2}

                                                                                                          _______________________________________________________________________________________________________________________________________________________
                                                                                                         /             ______________________                                                                                                                    
                                                                                                        /             /             ________                                                                                                                     
                                                                                                       /   49        /    343   7*\/ 199857                   14                                                      343                                        
                                                                                                      /    -- - 2*3 /   - --- + ------------  + ----------------------------- + -------------------------------------------------------------------------------- 
                    ____________________________________________________________________             /     2      \/       16       144                ______________________               ____________________________________________________________________ 
                   /             ______________________                                             /                                                 /             ________               /             ______________________                                  
                  /             /             ________                                             /                                                 /    343   7*\/ 199857               /             /             ________                                   
                 /   49        /    343   7*\/ 199857                   14                        /                                             3*3 /   - --- + ------------             /   49        /    343   7*\/ 199857                   14               
                /    -- + 2*3 /   - --- + ------------  - -----------------------------          /                                                \/       16       144         4*      /    -- + 2*3 /   - --- + ------------  - -----------------------------  
               /     4      \/       16       144                ______________________         /                                                                                      /     4      \/       16       144                ______________________  
              /                                                 /             ________         /                                                                                      /                                                 /             ________   
             /                                                 /    343   7*\/ 199857         /                                                                                      /                                                 /    343   7*\/ 199857    
            /                                             3*3 /   - --- + ------------       /                                                                                      /                                             3*3 /   - --- + ------------   
     21   \/                                                \/       16       144          \/                                                                                     \/                                                \/       16       144        
x4 = -- - ------------------------------------------------------------------------------ - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------
     4                                          2                                                                                                                            2

x_{4} = - \frac{\sqrt{- 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + \frac{49}{2} + \frac{343}{4 \sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}}}{2} - \frac{\sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}{2} + \frac{21}{4}

x4 = -sqrt(-2*(-343/16 + 7*sqrt(199857)/144)^(1/3) + 14/(3*(-343/16 + 7*sqrt(199857)/144)^(1/3)) + 49/2 + 343/(4*sqrt(-14/(3*(-343/16 + 7*sqrt(199857)/144)^(1/3)) + 2*(-343/16 + 7*sqrt(199857)/144)^(1/3) + 49/4)))/2 - sqrt(-14/(3*(-343/16 + 7*sqrt(199857)/144)^(1/3)) + 2*(-343/16 + 7*sqrt(199857)/144)^(1/3) + 49/4)/2 + 21/4

Sum and product of roots [src]

sum

                    _______________________________________________________________________________________________________________________________________________________                                                                                                                                                                                             ___________________________________________________________________________________________________________________________________________________________                                                                                                            ___________________________________________________________________________________________________________________________________________________________                                                                                                        _______________________________________________________________________________________________________________________________________________________
                   /             ______________________                                                                                                                                                                                                                                                                                                                /               ______________________                                                                                                                                                                                                                                 /               ______________________                                                                                                                                                                                                                             /             ______________________                                                                                                                    
                  /             /             ________                                                                                                                                                                                                                                                                                                                /               /             ________                                                                                                                                                                                                                                 /               /             ________                                                                                                                                                                                                                             /             /             ________                                                                                                                     
                 /   49        /    343   7*\/ 199857                   14                                                      343                                                                                                                                                                                                                                  /     49        /    343   7*\/ 199857                   14                                                       343                                                                                                                                                  /     49        /    343   7*\/ 199857                   14                                                       343                                                                                                                                              /   49        /    343   7*\/ 199857                   14                                                      343                                        
                /    -- - 2*3 /   - --- + ------------  + ----------------------------- + --------------------------------------------------------------------------------                                                                                                                                                                             I*           /    - -- + 2*3 /   - --- + ------------  - ----------------------------- + ----------------------------------------------------------------------------------                                                                                            I*           /    - -- + 2*3 /   - --- + ------------  - ----------------------------- + ----------------------------------------------------------------------------------                                                                                                     /    -- - 2*3 /   - --- + ------------  + ----------------------------- + -------------------------------------------------------------------------------- 
               /     2      \/       16       144                ______________________               ____________________________________________________________________              ____________________________________________________________________                  ______________________________________________________________________               /       2      \/       16       144                ______________________               ______________________________________________________________________                   ______________________________________________________________________               /       2      \/       16       144                ______________________               ______________________________________________________________________                   ____________________________________________________________________             /     2      \/       16       144                ______________________               ____________________________________________________________________ 
              /                                                 /             ________               /             ______________________                                              /             ______________________                                                  / |            ______________________                                |               /                                                   /             ________               / |            ______________________                                |                   / |            ______________________                                |               /                                                   /             ________               / |            ______________________                                |                   /             ______________________                                             /                                                 /             ________               /             ______________________                                  
             /                                                 /    343   7*\/ 199857               /             /             ________                                              /             /             ________                                                  /  |           /             ________                                 |              /                                                   /    343   7*\/ 199857               /  |           /             ________                                 |                  /  |           /             ________                                 |              /                                                   /    343   7*\/ 199857               /  |           /             ________                                 |                  /             /             ________                                             /                                                 /    343   7*\/ 199857               /             /             ________                                   
            /                                             3*3 /   - --- + ------------             /   49        /    343   7*\/ 199857                   14                         /   49        /    343   7*\/ 199857                   14                             /   |49        /    343   7*\/ 199857                   14             |             /                                               3*3 /   - --- + ------------             /   |49        /    343   7*\/ 199857                   14             |                 /   |49        /    343   7*\/ 199857                   14             |             /                                               3*3 /   - --- + ------------             /   |49        /    343   7*\/ 199857                   14             |                 /   49        /    343   7*\/ 199857                   14                        /                                             3*3 /   - --- + ------------             /   49        /    343   7*\/ 199857                   14               
           /                                                \/       16       144         4*      /    -- + 2*3 /   - --- + ------------  - -----------------------------           /    -- + 2*3 /   - --- + ------------  - -----------------------------               /    |-- + 2*3 /   - --- + ------------  - -----------------------------|            /                                                  \/       16       144         4*      /    |-- + 2*3 /   - --- + ------------  - -----------------------------|                /    |-- + 2*3 /   - --- + ------------  - -----------------------------|            /                                                  \/       16       144         4*      /    |-- + 2*3 /   - --- + ------------  - -----------------------------|                /    -- + 2*3 /   - --- + ------------  - -----------------------------          /                                                \/       16       144         4*      /    -- + 2*3 /   - --- + ------------  - -----------------------------  
          /                                                                                      /     4      \/       16       144                ______________________          /     4      \/       16       144                ______________________              /     |4      \/       16       144                ______________________|           /                                                                                        /     |4      \/       16       144                ______________________|               /     |4      \/       16       144                ______________________|           /                                                                                        /     |4      \/       16       144                ______________________|               /     4      \/       16       144                ______________________         /                                                                                      /     4      \/       16       144                ______________________  
         /                                                                                      /                                                 /             ________          /                                                 /             ________              /      |                                           /             ________ |          /                                                                                        /      |                                           /             ________ |              /      |                                           /             ________ |          /                                                                                        /      |                                           /             ________ |              /                                                 /             ________         /                                                                                      /                                                 /             ________   
        /                                                                                      /                                                 /    343   7*\/ 199857          /                                                 /    343   7*\/ 199857              /       |                                          /    343   7*\/ 199857  |         /                                                                                        /       |                                          /    343   7*\/ 199857  |             /       |                                          /    343   7*\/ 199857  |         /                                                                                        /       |                                          /    343   7*\/ 199857  |             /                                                 /    343   7*\/ 199857         /                                                                                      /                                                 /    343   7*\/ 199857    
       /                                                                                      /                                             3*3 /   - --- + ------------        /                                             3*3 /   - --- + ------------            /        |                                     3*3 /   - --- + ------------ |        /                                                                                        /        |                                     3*3 /   - --- + ------------ |            /        |                                     3*3 /   - --- + ------------ |        /                                                                                        /        |                                     3*3 /   - --- + ------------ |            /                                             3*3 /   - --- + ------------       /                                                                                      /                                             3*3 /   - --- + ------------   
21   \/                                                                                     \/                                                \/       16       144           \/                                                \/       16       144          21   \/         |                                       \/       16       144      |      \/                                                                                       \/         |                                       \/       16       144      |     21   \/         |                                       \/       16       144      |      \/                                                                                       \/         |                                       \/       16       144      |     21   \/                                                \/       16       144          \/                                                                                     \/                                                \/       16       144        
-- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------ + -- + -------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -- + -------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -- - ------------------------------------------------------------------------------ - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------
4                                                                                      2                                                                                                                            2                                          4                                           2                                                                                                                                2                                                                                         4                                           2                                                                                                                                2                                                                                         4                                          2                                                                                                                            2

\left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + \frac{49}{2} + \frac{343}{4 \sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}}}{2} - \frac{\sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}{2} + \frac{21}{4}\right) + \left(\left(\left(- \frac{\sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + \frac{49}{2} + \frac{343}{4 \sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}}}{2} + \frac{21}{4}\right) + \left(\frac{\sqrt{\left|{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}\right|}}{2} + \frac{21}{4} - \frac{i \sqrt{- \frac{49}{2} - \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{343}{4 \sqrt{\left|{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}\right|}}}}{2}\right)\right) + \left(\frac{\sqrt{\left|{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}\right|}}{2} + \frac{21}{4} + \frac{i \sqrt{- \frac{49}{2} - \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{343}{4 \sqrt{\left|{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}\right|}}}}{2}\right)\right)

               ______________________________________________________________________             ____________________________________________________________________
              / |            ______________________                                |             /             ______________________                                 
             /  |           /             ________                                 |            /             /             ________                                  
            /   |49        /    343   7*\/ 199857                   14             |           /   49        /    343   7*\/ 199857                   14              
21 +       /    |-- + 2*3 /   - --- + ------------  - -----------------------------|  -       /    -- + 2*3 /   - --- + ------------  - ----------------------------- 
          /     |4      \/       16       144                ______________________|         /     4      \/       16       144                ______________________ 
         /      |                                           /             ________ |        /                                                 /             ________  
        /       |                                          /    343   7*\/ 199857  |       /                                                 /    343   7*\/ 199857   
       /        |                                     3*3 /   - --- + ------------ |      /                                             3*3 /   - --- + ------------  
     \/         |                                       \/       16       144      |    \/                                                \/       16       144

- \sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}} + \sqrt{\left|{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}\right|} + 21

product

/                    _______________________________________________________________________________________________________________________________________________________                                                                                 \ /                                                                                                         ___________________________________________________________________________________________________________________________________________________________\ /                                                                                                         ___________________________________________________________________________________________________________________________________________________________\ /                                                                                                     _______________________________________________________________________________________________________________________________________________________\
|                   /             ______________________                                                                                                                                                                                                     | |                                                                                                        /               ______________________                                                                                                                      | |                                                                                                        /               ______________________                                                                                                                      | |                                                                                                    /             ______________________                                                                                                                    |
|                  /             /             ________                                                                                                                                                                                                      | |                                                                                                       /               /             ________                                                                                                                       | |                                                                                                       /               /             ________                                                                                                                       | |                                                                                                   /             /             ________                                                                                                                     |
|                 /   49        /    343   7*\/ 199857                   14                                                      343                                                                                                                         | |                                                                                                      /     49        /    343   7*\/ 199857                   14                                                       343                                         | |                                                                                                      /     49        /    343   7*\/ 199857                   14                                                       343                                         | |                                                                                                  /   49        /    343   7*\/ 199857                   14                                                      343                                        |
|                /    -- - 2*3 /   - --- + ------------  + ----------------------------- + --------------------------------------------------------------------------------                                                                                  | |                                                                                        I*           /    - -- + 2*3 /   - --- + ------------  - ----------------------------- + ---------------------------------------------------------------------------------- | |                                                                                        I*           /    - -- + 2*3 /   - --- + ------------  - ----------------------------- + ---------------------------------------------------------------------------------- | |                                                                                                 /    -- - 2*3 /   - --- + ------------  + ----------------------------- + -------------------------------------------------------------------------------- |
|               /     2      \/       16       144                ______________________               ____________________________________________________________________              ____________________________________________________________________| |               ______________________________________________________________________               /       2      \/       16       144                ______________________               ______________________________________________________________________ | |               ______________________________________________________________________               /       2      \/       16       144                ______________________               ______________________________________________________________________ | |               ____________________________________________________________________             /     2      \/       16       144                ______________________               ____________________________________________________________________ |
|              /                                                 /             ________               /             ______________________                                              /             ______________________                                 | |              / |            ______________________                                |               /                                                   /             ________               / |            ______________________                                |  | |              / |            ______________________                                |               /                                                   /             ________               / |            ______________________                                |  | |              /             ______________________                                             /                                                 /             ________               /             ______________________                                  |
|             /                                                 /    343   7*\/ 199857               /             /             ________                                              /             /             ________                                  | |             /  |           /             ________                                 |              /                                                   /    343   7*\/ 199857               /  |           /             ________                                 |  | |             /  |           /             ________                                 |              /                                                   /    343   7*\/ 199857               /  |           /             ________                                 |  | |             /             /             ________                                             /                                                 /    343   7*\/ 199857               /             /             ________                                   |
|            /                                             3*3 /   - --- + ------------             /   49        /    343   7*\/ 199857                   14                         /   49        /    343   7*\/ 199857                   14              | |            /   |49        /    343   7*\/ 199857                   14             |             /                                               3*3 /   - --- + ------------             /   |49        /    343   7*\/ 199857                   14             |  | |            /   |49        /    343   7*\/ 199857                   14             |             /                                               3*3 /   - --- + ------------             /   |49        /    343   7*\/ 199857                   14             |  | |            /   49        /    343   7*\/ 199857                   14                        /                                             3*3 /   - --- + ------------             /   49        /    343   7*\/ 199857                   14               |
|           /                                                \/       16       144         4*      /    -- + 2*3 /   - --- + ------------  - -----------------------------           /    -- + 2*3 /   - --- + ------------  - ----------------------------- | |           /    |-- + 2*3 /   - --- + ------------  - -----------------------------|            /                                                  \/       16       144         4*      /    |-- + 2*3 /   - --- + ------------  - -----------------------------|  | |           /    |-- + 2*3 /   - --- + ------------  - -----------------------------|            /                                                  \/       16       144         4*      /    |-- + 2*3 /   - --- + ------------  - -----------------------------|  | |           /    -- + 2*3 /   - --- + ------------  - -----------------------------          /                                                \/       16       144         4*      /    -- + 2*3 /   - --- + ------------  - -----------------------------  |
|          /                                                                                      /     4      \/       16       144                ______________________          /     4      \/       16       144                ______________________ | |          /     |4      \/       16       144                ______________________|           /                                                                                        /     |4      \/       16       144                ______________________|  | |          /     |4      \/       16       144                ______________________|           /                                                                                        /     |4      \/       16       144                ______________________|  | |          /     4      \/       16       144                ______________________         /                                                                                      /     4      \/       16       144                ______________________  |
|         /                                                                                      /                                                 /             ________          /                                                 /             ________  | |         /      |                                           /             ________ |          /                                                                                        /      |                                           /             ________ |  | |         /      |                                           /             ________ |          /                                                                                        /      |                                           /             ________ |  | |         /                                                 /             ________         /                                                                                      /                                                 /             ________   |
|        /                                                                                      /                                                 /    343   7*\/ 199857          /                                                 /    343   7*\/ 199857   | |        /       |                                          /    343   7*\/ 199857  |         /                                                                                        /       |                                          /    343   7*\/ 199857  |  | |        /       |                                          /    343   7*\/ 199857  |         /                                                                                        /       |                                          /    343   7*\/ 199857  |  | |        /                                                 /    343   7*\/ 199857         /                                                                                      /                                                 /    343   7*\/ 199857    |
|       /                                                                                      /                                             3*3 /   - --- + ------------        /                                             3*3 /   - --- + ------------  | |       /        |                                     3*3 /   - --- + ------------ |        /                                                                                        /        |                                     3*3 /   - --- + ------------ |  | |       /        |                                     3*3 /   - --- + ------------ |        /                                                                                        /        |                                     3*3 /   - --- + ------------ |  | |       /                                             3*3 /   - --- + ------------       /                                                                                      /                                             3*3 /   - --- + ------------   |
|21   \/                                                                                     \/                                                \/       16       144           \/                                                \/       16       144       | |21   \/         |                                       \/       16       144      |      \/                                                                                       \/         |                                       \/       16       144      |  | |21   \/         |                                       \/       16       144      |      \/                                                                                       \/         |                                       \/       16       144      |  | |21   \/                                                \/       16       144          \/                                                                                     \/                                                \/       16       144        |
|-- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------|*|-- + -------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|-- + -------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|-- - ------------------------------------------------------------------------------ - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------|
\4                                                                                      2                                                                                                                            2                                       / \4                                           2                                                                                                                                2                                                                                      / \4                                           2                                                                                                                                2                                                                                      / \4                                          2                                                                                                                            2                                                                                   /

\left(- \frac{\sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + \frac{49}{2} + \frac{343}{4 \sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}}}{2} + \frac{21}{4}\right) \left(\frac{\sqrt{\left|{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}\right|}}{2} + \frac{21}{4} - \frac{i \sqrt{- \frac{49}{2} - \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{343}{4 \sqrt{\left|{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}\right|}}}}{2}\right) \left(\frac{\sqrt{\left|{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}\right|}}{2} + \frac{21}{4} + \frac{i \sqrt{- \frac{49}{2} - \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{343}{4 \sqrt{\left|{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}\right|}}}}{2}\right) \left(- \frac{\sqrt{- 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + \frac{49}{2} + \frac{343}{4 \sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}}}{2} - \frac{\sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}{2} + \frac{21}{4}\right)

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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |                                                                                                           /                                                                         343*|------------------------------------------------------------------------------| | |                                                                                                           /                                                                         343*|------------------------------------------------------------------------------| |
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 /                                                                                                       _______________________________________________________________________________________________________________________________________________________\ /                    _______________________________________________________________________________________________________________________________________________________                                                                                 \ |                                                                                                         /                                                                               |         /             ______________________                                 | | |                                                                                                         /                                                                               |         /             ______________________                                 | |
 |                                                                                                      /             ______________________                                                                                                                    | |                   /             ______________________                                                                                                                                                                                                     | |                                                                                                        /                                                                                |        /             /             ________                                  | | |                                                                                                        /                                                                                |        /             /             ________                                  | |
 |                                                                                                     /             /             ________                                                                                                                     | |                  /             /             ________                                                                                                                                                                                                      | |                                                                                                       /                                                                                 |       /   49        /    343   7*\/ 199857                   14              | | |                                                                                                       /                                                                                 |       /   49        /    343   7*\/ 199857                   14              | |
 |                                                                                                    /   49        /    343   7*\/ 199857                   14                                                      343                                        | |                 /   49        /    343   7*\/ 199857                   14                                                      343                                                                                                                         | |                                                                                                      /                                                                                  |      /    -- + 2*3 /   - --- + ------------  - ----------------------------- | | |                                                                                                      /                                                                                  |      /    -- + 2*3 /   - --- + ------------  - ----------------------------- | |
 |                                                                                                   /    -- - 2*3 /   - --- + ------------  + ----------------------------- + -------------------------------------------------------------------------------- | |                /    -- - 2*3 /   - --- + ------------  + ----------------------------- + --------------------------------------------------------------------------------                                                                                  | |                                                                                                     /                                                                                   |     /     4      \/       16       144                ______________________ | | |                                                                                                     /                                                                                   |     /     4      \/       16       144                ______________________ | |
 |                 ____________________________________________________________________             /     2      \/       16       144                ______________________               ____________________________________________________________________ | |               /     2      \/       16       144                ______________________               ____________________________________________________________________              ____________________________________________________________________| |               ______________________________________________________________________               /                                                                                    |    /                                                 /             ________  | | |               ______________________________________________________________________               /                                                                                    |    /                                                 /             ________  | |
 |                /             ______________________                                             /                                                 /             ________               /             ______________________                                  | |              /                                                 /             ________               /             ______________________                                              /             ______________________                                 | |              / |            ______________________                                |               /                        ______________________                                       |   /                                                 /    343   7*\/ 199857   | | |              / |            ______________________                                |               /                        ______________________                                       |   /                                                 /    343   7*\/ 199857   | |
 |               /             /             ________                                             /                                                 /    343   7*\/ 199857               /             /             ________                                   | |             /                                                 /    343   7*\/ 199857               /             /             ________                                              /             /             ________                                  | |             /  |           /             ________                                 |              /                        /             ________                                        |  /                                             3*3 /   - --- + ------------  | | |             /  |           /             ________                                 |              /                        /             ________                                        |  /                                             3*3 /   - --- + ------------  | |
 |              /   49        /    343   7*\/ 199857                   14                        /                                             3*3 /   - --- + ------------             /   49        /    343   7*\/ 199857                   14               | |            /                                             3*3 /   - --- + ------------             /   49        /    343   7*\/ 199857                   14                         /   49        /    343   7*\/ 199857                   14              | |            /   |49        /    343   7*\/ 199857                   14             |             /              49        /    343   7*\/ 199857                   14                    |\/                                                \/       16       144       | | |            /   |49        /    343   7*\/ 199857                   14             |             /              49        /    343   7*\/ 199857                   14                    |\/                                                \/       16       144       | |
 |             /    -- + 2*3 /   - --- + ------------  - -----------------------------          /                                                \/       16       144         4*      /    -- + 2*3 /   - --- + ------------  - -----------------------------  | |           /                                                \/       16       144         4*      /    -- + 2*3 /   - --- + ------------  - -----------------------------           /    -- + 2*3 /   - --- + ------------  - ----------------------------- | |           /    |-- + 2*3 /   - --- + ------------  - -----------------------------|    I*      /             - -- + 2*3 /   - --- + ------------  - ----------------------------- + ------------------------------------------------------------------------------------ | |           /    |-- + 2*3 /   - --- + ------------  - -----------------------------|    I*      /             - -- + 2*3 /   - --- + ------------  - ----------------------------- + ------------------------------------------------------------------------------------ |
 |            /     4      \/       16       144                ______________________         /                                                                                      /     4      \/       16       144                ______________________  | |          /                                                                                      /     4      \/       16       144                ______________________          /     4      \/       16       144                ______________________ | |          /     |4      \/       16       144                ______________________|           /                2      \/       16       144                ______________________                                            4                                           | |          /     |4      \/       16       144                ______________________|           /                2      \/       16       144                ______________________                                            4                                           |
 |           /                                                 /             ________         /                                                                                      /                                                 /             ________   | |         /                                                                                      /                                                 /             ________          /                                                 /             ________  | |         /      |                                           /             ________ |          /                                                            /             ________                                                                                         | |         /      |                                           /             ________ |          /                                                            /             ________                                                                                         |
 |          /                                                 /    343   7*\/ 199857         /                                                                                      /                                                 /    343   7*\/ 199857    | |        /                                                                                      /                                                 /    343   7*\/ 199857          /                                                 /    343   7*\/ 199857   | |        /       |                                          /    343   7*\/ 199857  |         /                                                            /    343   7*\/ 199857                                                                                          | |        /       |                                          /    343   7*\/ 199857  |         /                                                            /    343   7*\/ 199857                                                                                          |
 |         /                                             3*3 /   - --- + ------------       /                                                                                      /                                             3*3 /   - --- + ------------   | |       /                                                                                      /                                             3*3 /   - --- + ------------        /                                             3*3 /   - --- + ------------  | |       /        |                                     3*3 /   - --- + ------------ |        /                                                        3*3 /   - --- + ------------                                                                                         | |       /        |                                     3*3 /   - --- + ------------ |        /                                                        3*3 /   - --- + ------------                                                                                         |
 |  21   \/                                                \/       16       144          \/                                                                                     \/                                                \/       16       144        | |21   \/                                                                                     \/                                                \/       16       144           \/                                                \/       16       144       | |21   \/         |                                       \/       16       144      |      \/                                                           \/       16       144                                                                                              | |21   \/         |                                       \/       16       144      |      \/                                                           \/       16       144                                                                                              |
-|- -- + ------------------------------------------------------------------------------ + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|-- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------|*|-- + -------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*|-- + -------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
 \  4                                          2                                                                                                                            2                                                                                   / \4                                                                                      2                                                                                                                            2                                       / \4                                           2                                                                                                                                   2                                                                                         / \4                                           2                                                                                                                                   2                                                                                         /

- \left(- \frac{21}{4} + \frac{\sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + \frac{49}{2} + \frac{343}{4 \sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}}}{2}\right) \left(- \frac{\sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + \frac{49}{2} + \frac{343}{4 \sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}}}{2} + \frac{21}{4}\right) \left(\frac{\sqrt{\left|{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}\right|}}{2} + \frac{21}{4} - \frac{i \sqrt{- \frac{49}{2} - \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{343 \left|{\frac{1}{\sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}}\right|}{4}}}{2}\right) \left(\frac{\sqrt{\left|{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}\right|}}{2} + \frac{21}{4} + \frac{i \sqrt{- \frac{49}{2} - \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{343 \left|{\frac{1}{\sqrt{- \frac{14}{3 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}}} + 2 \sqrt[3]{- \frac{343}{16} + \frac{7 \sqrt{199857}}{144}} + \frac{49}{4}}}}\right|}{4}}}{2}\right)

-(-21/4 + sqrt(49/4 + 2*(-343/16 + 7*sqrt(199857)/144)^(1/3) - 14/(3*(-343/16 + 7*sqrt(199857)/144)^(1/3)))/2 + sqrt(49/2 - 2*(-343/16 + 7*sqrt(199857)/144)^(1/3) + 14/(3*(-343/16 + 7*sqrt(199857)/144)^(1/3)) + 343/(4*sqrt(49/4 + 2*(-343/16 + 7*sqrt(199857)/144)^(1/3) - 14/(3*(-343/16 + 7*sqrt(199857)/144)^(1/3)))))/2)*(21/4 + sqrt(49/2 - 2*(-343/16 + 7*sqrt(199857)/144)^(1/3) + 14/(3*(-343/16 + 7*sqrt(199857)/144)^(1/3)) + 343/(4*sqrt(49/4 + 2*(-343/16 + 7*sqrt(199857)/144)^(1/3) - 14/(3*(-343/16 + 7*sqrt(199857)/144)^(1/3)))))/2 - sqrt(49/4 + 2*(-343/16 + 7*sqrt(199857)/144)^(1/3) - 14/(3*(-343/16 + 7*sqrt(199857)/144)^(1/3)))/2)*(21/4 + sqrt(Abs(49/4 + 2*(-343/16 + 7*sqrt(199857)/144)^(1/3) - 14/(3*(-343/16 + 7*sqrt(199857)/144)^(1/3))))/2 + i*sqrt(-49/2 + 2*(-343/16 + 7*sqrt(199857)/144)^(1/3) - 14/(3*(-343/16 + 7*sqrt(199857)/144)^(1/3)) + 343*Abs(1/sqrt(49/4 + 2*(-343/16 + 7*sqrt(199857)/144)^(1/3) - 14/(3*(-343/16 + 7*sqrt(199857)/144)^(1/3))))/4)/2)*(21/4 + sqrt(Abs(49/4 + 2*(-343/16 + 7*sqrt(199857)/144)^(1/3) - 14/(3*(-343/16 + 7*sqrt(199857)/144)^(1/3))))/2 - i*sqrt(-49/2 + 2*(-343/16 + 7*sqrt(199857)/144)^(1/3) - 14/(3*(-343/16 + 7*sqrt(199857)/144)^(1/3)) + 343*Abs(1/sqrt(49/4 + 2*(-343/16 + 7*sqrt(199857)/144)^(1/3) - 14/(3*(-343/16 + 7*sqrt(199857)/144)^(1/3))))/4)/2)

Numerical answer [src]

x1 = 7.95813968267176

x2 = 6.5310462701994 - 0.90596007603433*i

x3 = 6.5310462701994 + 0.90596007603433*i

x4 = -0.0202322230705539

x4 = -0.0202322230705539

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x+7/(7-x)^3=0 equation

Numerical solution:

The solution