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Equation:
Equation 4x^4-5x^2+1=0
Equation x^(2)-12+(36/X^(2))+2((x/2)-(3/x))=0
Equation 9x^3-18x=x-2
Equation 3y^2+y-24/9-y^2=-2
Express {x} in terms of y where:
9*x+18*y=6
15*x-15*y=16
sqrt(x^2+y^2+4x-6y-12)+(x^2+10x-27)=8-|y-9|+|y-3|
(x^2+y^2-1)^3+x^2*y^3=0
Derivative of:
x-2
The double integral of:
x-2
Graphing y =:
x-2
Identical expressions
9x^ three -18x=x- two
9x cubed minus 18x equally x minus 2
9x to the power of three minus 18x equally x minus two
9x3-18x=x-2
9x³-18x=x-2
9x to the power of 3-18x=x-2
Similar expressions
9x^3-18x=x+2
9x^3+18x=x-2

9x^3-18x=x-2 equation

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

The solution

You have entered [src]

   3               
9*x  - 18*x = x - 2

9 x^{3} - 18 x = x - 2

Simplify

Vieta's Theorem

rewrite the equation

9 x^{3} - 18 x = x - 2

a x^{3} + b x^{2} + c x + d = 0

as reduced cubic equation

x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0

x^{3} - \frac{19 x}{9} + \frac{2}{9} = 0

p x^{2} + q x + v + x^{3} = 0

where

p = \frac{b}{a}

p = 0

q = \frac{c}{a}

q = - \frac{19}{9}

v = \frac{d}{a}

v = \frac{2}{9}

Vieta Formulas

x_{1} + x_{2} + x_{3} = - p

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q

x_{1} x_{2} x_{3} = v

x_{1} + x_{2} + x_{3} = 0

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = - \frac{19}{9}

x_{1} x_{2} x_{3} = \frac{2}{9}

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Sum and product of roots [src]

sum

       /                   1                   \     /       /                   1                   \                                                              \                                                                        /                   1                   \     /       /                   1                   \                                                              \                                                                                                                      
  19*re|---------------------------------------|     |  19*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|             /    /    ______\\             /    /    ______\\     19*re|---------------------------------------|     |  19*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|             /    /    ______\\             /    /    ______\\                                                        
       |     __________________                |     |       |     __________________                |             |    |2*\/ 4962 ||             |    |2*\/ 4962 |||             |    |2*\/ 4962 ||             |    |2*\/ 4962 ||          |     __________________                |     |       |     __________________                |             |    |2*\/ 4962 ||             |    |2*\/ 4962 |||             |    |2*\/ 4962 ||             |    |2*\/ 4962 ||                                      __________________
       |    /           ______  /          ___\|     |       |    /           ______  /          ___\|             |atan|----------||             |atan|----------|||             |atan|----------||             |atan|----------||          |    /           ______  /          ___\|     |       |    /           ______  /          ___\|             |atan|----------||             |atan|----------|||             |atan|----------||             |atan|----------||                                     /           ______ 
       |   /      2*I*\/ 4962   |  1   I*\/ 3 ||     |       |   /      2*I*\/ 4962   |  1   I*\/ 3 ||     ____    |    \    27    /|     ____    |    \    27    /||     ____    |    \    27    /|     ____    |    \    27    /|          |   /      2*I*\/ 4962   |  1   I*\/ 3 ||     |       |   /      2*I*\/ 4962   |  1   I*\/ 3 ||     ____    |    \    27    /|     ____    |    \    27    /||     ____    |    \    27    /|     ____    |    \    27    /|                                    /      2*I*\/ 4962  
       |3 /   3 + ------------ *|- - - -------||     |       |3 /   3 + ------------ *|- - - -------||   \/ 19 *cos|----------------|   \/ 57 *sin|----------------||   \/ 19 *sin|----------------|   \/ 57 *cos|----------------|          |3 /   3 + ------------ *|- - + -------||     |       |3 /   3 + ------------ *|- - + -------||   \/ 19 *cos|----------------|   \/ 57 *sin|----------------||   \/ 19 *sin|----------------|   \/ 57 *cos|----------------|                                 3 /   3 + ------------ 
       \\/             9        \  2      2   //     |       \\/             9        \  2      2   //             \       3        /             \       3        /|             \       3        /             \       3        /          \\/             9        \  2      2   //     |       \\/             9        \  2      2   //             \       3        /             \       3        /|             \       3        /             \       3        /                 19              \/             9       
- ---------------------------------------------- + I*|- ---------------------------------------------- + ---------------------------- + ----------------------------| - ---------------------------- + ---------------------------- + - ---------------------------------------------- + I*|- ---------------------------------------------- - ---------------------------- + ----------------------------| + ---------------------------- + ---------------------------- + - ------------------------- - -----------------------
                        9                            \                        9                                       6                              18             /                6                              18                                        9                            \                        9                                       6                              18             /                6                              18                         __________________              3           
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    /           ______                           
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   /      2*I*\/ 4962                            
                                                                                                                                                                                                                                                                                                                                                                                                                                                                              9*3 /   3 + ------------                           
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                \/             9

\left(\left(- \frac{\sqrt{19} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} - \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} + i \left(- \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} + \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6}\right)\right) + \left(\frac{\sqrt{19} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} + \frac{\sqrt{57} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} - \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + i \left(- \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} - \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9}\right)\right)\right) + \left(- \frac{\sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}{3} - \frac{19}{9 \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)

                                   /                   1                   \        /                   1                   \                               /       /                   1                   \                                                              \     /       /                   1                   \                                                              \                               
                              19*re|---------------------------------------|   19*re|---------------------------------------|                               |  19*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|     |  19*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|             /    /    ______\\
                                   |     __________________                |        |     __________________                |        __________________     |       |     __________________                |             |    |2*\/ 4962 ||             |    |2*\/ 4962 |||     |       |     __________________                |             |    |2*\/ 4962 ||             |    |2*\/ 4962 |||             |    |2*\/ 4962 ||
                                   |    /           ______  /          ___\|        |    /           ______  /          ___\|       /           ______      |       |    /           ______  /          ___\|             |atan|----------||             |atan|----------|||     |       |    /           ______  /          ___\|             |atan|----------||             |atan|----------|||             |atan|----------||
                                   |   /      2*I*\/ 4962   |  1   I*\/ 3 ||        |   /      2*I*\/ 4962   |  1   I*\/ 3 ||      /      2*I*\/ 4962       |       |   /      2*I*\/ 4962   |  1   I*\/ 3 ||     ____    |    \    27    /|     ____    |    \    27    /||     |       |   /      2*I*\/ 4962   |  1   I*\/ 3 ||     ____    |    \    27    /|     ____    |    \    27    /||     ____    |    \    27    /|
                                   |3 /   3 + ------------ *|- - + -------||        |3 /   3 + ------------ *|- - - -------||   3 /   3 + ------------      |       |3 /   3 + ------------ *|- - + -------||   \/ 19 *cos|----------------|   \/ 57 *sin|----------------||     |       |3 /   3 + ------------ *|- - - -------||   \/ 19 *cos|----------------|   \/ 57 *sin|----------------||   \/ 57 *cos|----------------|
              19                   \\/             9        \  2      2   //        \\/             9        \  2      2   //   \/             9            |       \\/             9        \  2      2   //             \       3        /             \       3        /|     |       \\/             9        \  2      2   //             \       3        /             \       3        /|             \       3        /
- ------------------------- - ---------------------------------------------- - ---------------------------------------------- - ----------------------- + I*|- ---------------------------------------------- - ---------------------------- + ----------------------------| + I*|- ---------------------------------------------- + ---------------------------- + ----------------------------| + ----------------------------
         __________________                         9                                                9                                     3                \                        9                                       6                              18             /     \                        9                                       6                              18             /                9              
        /           ______                                                                                                                                                                                                                                                                                                                                                                                                      
       /      2*I*\/ 4962                                                                                                                                                                                                                                                                                                                                                                                                       
  9*3 /   3 + ------------                                                                                                                                                                                                                                                                                                                                                                                                      
    \/             9

- \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} - \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{9} - \frac{\sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}{3} + i \left(- \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} - \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9}\right) + i \left(- \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} + \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6}\right) - \frac{19}{9 \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}

product

/       /                   1                   \     /       /                   1                   \                                                              \                                                              \ /       /                   1                   \     /       /                   1                   \                                                              \                                                              \                                                        
|  19*re|---------------------------------------|     |  19*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|             /    /    ______\\             /    /    ______\\| |  19*re|---------------------------------------|     |  19*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|             /    /    ______\\             /    /    ______\\|                                                        
|       |     __________________                |     |       |     __________________                |             |    |2*\/ 4962 ||             |    |2*\/ 4962 |||             |    |2*\/ 4962 ||             |    |2*\/ 4962 ||| |       |     __________________                |     |       |     __________________                |             |    |2*\/ 4962 ||             |    |2*\/ 4962 |||             |    |2*\/ 4962 ||             |    |2*\/ 4962 ||| /                                   __________________\
|       |    /           ______  /          ___\|     |       |    /           ______  /          ___\|             |atan|----------||             |atan|----------|||             |atan|----------||             |atan|----------||| |       |    /           ______  /          ___\|     |       |    /           ______  /          ___\|             |atan|----------||             |atan|----------|||             |atan|----------||             |atan|----------||| |                                  /           ______ |
|       |   /      2*I*\/ 4962   |  1   I*\/ 3 ||     |       |   /      2*I*\/ 4962   |  1   I*\/ 3 ||     ____    |    \    27    /|     ____    |    \    27    /||     ____    |    \    27    /|     ____    |    \    27    /|| |       |   /      2*I*\/ 4962   |  1   I*\/ 3 ||     |       |   /      2*I*\/ 4962   |  1   I*\/ 3 ||     ____    |    \    27    /|     ____    |    \    27    /||     ____    |    \    27    /|     ____    |    \    27    /|| |                                 /      2*I*\/ 4962  |
|       |3 /   3 + ------------ *|- - - -------||     |       |3 /   3 + ------------ *|- - - -------||   \/ 19 *cos|----------------|   \/ 57 *sin|----------------||   \/ 19 *sin|----------------|   \/ 57 *cos|----------------|| |       |3 /   3 + ------------ *|- - + -------||     |       |3 /   3 + ------------ *|- - + -------||   \/ 19 *cos|----------------|   \/ 57 *sin|----------------||   \/ 19 *sin|----------------|   \/ 57 *cos|----------------|| |                              3 /   3 + ------------ |
|       \\/             9        \  2      2   //     |       \\/             9        \  2      2   //             \       3        /             \       3        /|             \       3        /             \       3        /| |       \\/             9        \  2      2   //     |       \\/             9        \  2      2   //             \       3        /             \       3        /|             \       3        /             \       3        /| |              19              \/             9       |
|- ---------------------------------------------- + I*|- ---------------------------------------------- + ---------------------------- + ----------------------------| - ---------------------------- + ----------------------------|*|- ---------------------------------------------- + I*|- ---------------------------------------------- - ---------------------------- + ----------------------------| + ---------------------------- + ----------------------------|*|- ------------------------- - -----------------------|
\                        9                            \                        9                                       6                              18             /                6                              18             / \                        9                            \                        9                                       6                              18             /                6                              18             / |         __________________              3           |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |        /           ______                           |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |       /      2*I*\/ 4962                            |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |  9*3 /   3 + ------------                           |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \    \/             9                                 /

\left(- \frac{\sqrt{19} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} - \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} + i \left(- \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} + \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6}\right)\right) \left(\frac{\sqrt{19} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} + \frac{\sqrt{57} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} - \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + i \left(- \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} - \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9}\right)\right) \left(- \frac{\sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}{3} - \frac{19}{9 \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)

         /         /      /    ______\\\                                    
         |         |      |2*\/ 4962 |||                                    
         |         |2*atan|----------||| /                   2/3           \
   3 ___ |         |      \    27    /|| |/           ______\         3 ___|
19*\/ 3 *|1 - 2*cos|------------------||*\\27 + 2*I*\/ 4962 /    + 19*\/ 3 /
         \         \        3         //                                    
----------------------------------------------------------------------------
                                ___________________                         
                             3 /            ______                          
                         243*\/  27 + 2*I*\/ 4962

\frac{19 \sqrt[3]{3} \left(1 - 2 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}\right) \left(19 \sqrt[3]{3} + \left(27 + 2 \sqrt{4962} i\right)^{\frac{2}{3}}\right)}{243 \sqrt[3]{27 + 2 \sqrt{4962} i}}

19*3^(1/3)*(1 - 2*cos(2*atan(2*sqrt(4962)/27)/3))*((27 + 2*i*sqrt(4962))^(2/3) + 19*3^(1/3))/(243*(27 + 2*i*sqrt(4962))^(1/3))

Rapid solution [src]

            /                   1                   \     /       /                   1                   \                                                              \                                                              
       19*re|---------------------------------------|     |  19*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|             /    /    ______\\             /    /    ______\\
            |     __________________                |     |       |     __________________                |             |    |2*\/ 4962 ||             |    |2*\/ 4962 |||             |    |2*\/ 4962 ||             |    |2*\/ 4962 ||
            |    /           ______  /          ___\|     |       |    /           ______  /          ___\|             |atan|----------||             |atan|----------|||             |atan|----------||             |atan|----------||
            |   /      2*I*\/ 4962   |  1   I*\/ 3 ||     |       |   /      2*I*\/ 4962   |  1   I*\/ 3 ||     ____    |    \    27    /|     ____    |    \    27    /||     ____    |    \    27    /|     ____    |    \    27    /|
            |3 /   3 + ------------ *|- - - -------||     |       |3 /   3 + ------------ *|- - - -------||   \/ 19 *cos|----------------|   \/ 57 *sin|----------------||   \/ 19 *sin|----------------|   \/ 57 *cos|----------------|
            \\/             9        \  2      2   //     |       \\/             9        \  2      2   //             \       3        /             \       3        /|             \       3        /             \       3        /
x1 = - ---------------------------------------------- + I*|- ---------------------------------------------- + ---------------------------- + ----------------------------| - ---------------------------- + ----------------------------
                             9                            \                        9                                       6                              18             /                6                              18

x_{1} = - \frac{\sqrt{19} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} - \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} + i \left(- \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} + \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6}\right)

            /                   1                   \     /       /                   1                   \                                                              \                                                              
       19*re|---------------------------------------|     |  19*im|---------------------------------------|             /    /    ______\\             /    /    ______\\|             /    /    ______\\             /    /    ______\\
            |     __________________                |     |       |     __________________                |             |    |2*\/ 4962 ||             |    |2*\/ 4962 |||             |    |2*\/ 4962 ||             |    |2*\/ 4962 ||
            |    /           ______  /          ___\|     |       |    /           ______  /          ___\|             |atan|----------||             |atan|----------|||             |atan|----------||             |atan|----------||
            |   /      2*I*\/ 4962   |  1   I*\/ 3 ||     |       |   /      2*I*\/ 4962   |  1   I*\/ 3 ||     ____    |    \    27    /|     ____    |    \    27    /||     ____    |    \    27    /|     ____    |    \    27    /|
            |3 /   3 + ------------ *|- - + -------||     |       |3 /   3 + ------------ *|- - + -------||   \/ 19 *cos|----------------|   \/ 57 *sin|----------------||   \/ 19 *sin|----------------|   \/ 57 *cos|----------------|
            \\/             9        \  2      2   //     |       \\/             9        \  2      2   //             \       3        /             \       3        /|             \       3        /             \       3        /
x2 = - ---------------------------------------------- + I*|- ---------------------------------------------- - ---------------------------- + ----------------------------| + ---------------------------- + ----------------------------
                             9                            \                        9                                       6                              18             /                6                              18

x_{2} = \frac{\sqrt{19} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} + \frac{\sqrt{57} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} - \frac{19 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9} + i \left(- \frac{\sqrt{19} \cos{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{6} + \frac{\sqrt{57} \sin{\left(\frac{\operatorname{atan}{\left(\frac{2 \sqrt{4962}}{27} \right)}}{3} \right)}}{18} - \frac{19 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}\right)}}{9}\right)

                                        __________________
                                       /           ______ 
                                      /      2*I*\/ 4962  
                                   3 /   3 + ------------ 
                   19              \/             9       
x3 = - ------------------------- - -----------------------
              __________________              3           
             /           ______                           
            /      2*I*\/ 4962                            
       9*3 /   3 + ------------                           
         \/             9

x_{3} = - \frac{\sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}{3} - \frac{19}{9 \sqrt[3]{3 + \frac{2 \sqrt{4962} i}{9}}}

x3 = -(3 + 2*sqrt(4962)*i/9)^(1/3)/3 - 19/(9*(3 + 2*sqrt(4962)*i/9)^(1/3))

Numerical answer [src]

x1 = -1.50298536069965

x2 = 0.10582452622341

x3 = 1.39716083447624

x3 = 1.39716083447624

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9x^3-18x=x-2 equation

Numerical solution:

The solution