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Identical expressions
- x^ three - seven *x^ two - four *x+ thirty-two = zero
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Similar expressions
- x^3+7*x^2-4*x+32=0
- x^3-7*x^2+4*x+32=0
- x^3-7*x^2-4*x-32=0
x^3-7*x^2-4*x+32=0 equation
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The solution
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[src]
3 2 x - 7*x - 4*x + 32 = 0
$$\left(- 4 x + \left(x^{3} - 7 x^{2}\right)\right) + 32 = 0$$
Vieta's Theorem
it is reduced cubic equation
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -7$$
$$q = \frac{c}{a}$$
$$q = -4$$
$$v = \frac{d}{a}$$
$$v = 32$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 7$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -4$$
$$x_{1} x_{2} x_{3} = 32$$
$$p x^{2} + q x + v + x^{3} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -7$$
$$q = \frac{c}{a}$$
$$q = -4$$
$$v = \frac{d}{a}$$
$$v = 32$$
Vieta Formulas
$$x_{1} + x_{2} + x_{3} = - p$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q$$
$$x_{1} x_{2} x_{3} = v$$
$$x_{1} + x_{2} + x_{3} = 7$$
$$x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -4$$
$$x_{1} x_{2} x_{3} = 32$$
Rapid solution
[src]
/ 1 \ / / 1 \ \
61*re|----------------------------------------| |61*im|----------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| ___________________| | | ___________________| | |6*\/ 6267 || | |6*\/ 6267 ||| | |6*\/ 6267 || | |6*\/ 6267 ||
|/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
|| 1 I*\/ 3 | / 37 2*I*\/ 6267 | | || 1 I*\/ 3 | / 37 2*I*\/ 6267 | ____ | \ 37 /| _____ | \ 37 /|| ____ | \ 37 /| _____ | \ 37 /|
||- - - -------|*3 / -- + ------------ | | ||- - - -------|*3 / -- + ------------ | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| \/ 61 *cos|----------------| \/ 183 *sin|----------------|
7 \\ 2 2 / \/ 27 9 / | \\ 2 2 / \/ 27 9 / \ 3 / \ 3 /| \ 3 / \ 3 /
x1 = - + ----------------------------------------------- + I*|----------------------------------------------- - ---------------------------- - -----------------------------| - ---------------------------- + -----------------------------
3 9 \ 9 6 6 / 6 6
$$x_{1} = - \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9} + \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{7}{3} + i \left(- \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9}\right)$$
/ 1 \ / / 1 \ \
61*re|----------------------------------------| |61*im|----------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| ___________________| | | ___________________| | |6*\/ 6267 || | |6*\/ 6267 ||| | |6*\/ 6267 || | |6*\/ 6267 ||
|/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
|| 1 I*\/ 3 | / 37 2*I*\/ 6267 | | || 1 I*\/ 3 | / 37 2*I*\/ 6267 | ____ | \ 37 /| _____ | \ 37 /|| ____ | \ 37 /| _____ | \ 37 /|
||- - + -------|*3 / -- + ------------ | | ||- - + -------|*3 / -- + ------------ | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| \/ 61 *cos|----------------| \/ 183 *sin|----------------|
7 \\ 2 2 / \/ 27 9 / | \\ 2 2 / \/ 27 9 / \ 3 / \ 3 /| \ 3 / \ 3 /
x2 = - + ----------------------------------------------- + I*|----------------------------------------------- - ---------------------------- + -----------------------------| - ---------------------------- - -----------------------------
3 9 \ 9 6 6 / 6 6
$$x_{2} = \frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9} - \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} - \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{7}{3} + i \left(\frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6}\right)$$
___________________
/ ______
7 / 37 2*I*\/ 6267 61
x3 = - + 3 / -- + ------------ + --------------------------
3 \/ 27 9 ___________________
/ ______
/ 37 2*I*\/ 6267
9*3 / -- + ------------
\/ 27 9
$$x_{3} = \frac{7}{3} + \frac{61}{9 \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}} + \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}$$
x3 = 7/3 + 61/(9*(37/27 + 2*sqrt(6267)*i/9)^(1/3)) + (37/27 + 2*sqrt(6267)*i/9)^(1/3)
Sum and product of roots
[src]
sum
/ 1 \ / / 1 \ \ / 1 \ / / 1 \ \
61*re|----------------------------------------| |61*im|----------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\ 61*re|----------------------------------------| |61*im|----------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\
| ___________________| | | ___________________| | |6*\/ 6267 || | |6*\/ 6267 ||| | |6*\/ 6267 || | |6*\/ 6267 || | ___________________| | | ___________________| | |6*\/ 6267 || | |6*\/ 6267 ||| | |6*\/ 6267 || | |6*\/ 6267 ||
|/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|| |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||
|| 1 I*\/ 3 | / 37 2*I*\/ 6267 | | || 1 I*\/ 3 | / 37 2*I*\/ 6267 | ____ | \ 37 /| _____ | \ 37 /|| ____ | \ 37 /| _____ | \ 37 /| || 1 I*\/ 3 | / 37 2*I*\/ 6267 | | || 1 I*\/ 3 | / 37 2*I*\/ 6267 | ____ | \ 37 /| _____ | \ 37 /|| ____ | \ 37 /| _____ | \ 37 /| ___________________
||- - - -------|*3 / -- + ------------ | | ||- - - -------|*3 / -- + ------------ | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| \/ 61 *cos|----------------| \/ 183 *sin|----------------| ||- - + -------|*3 / -- + ------------ | | ||- - + -------|*3 / -- + ------------ | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| \/ 61 *cos|----------------| \/ 183 *sin|----------------| / ______
7 \\ 2 2 / \/ 27 9 / | \\ 2 2 / \/ 27 9 / \ 3 / \ 3 /| \ 3 / \ 3 / 7 \\ 2 2 / \/ 27 9 / | \\ 2 2 / \/ 27 9 / \ 3 / \ 3 /| \ 3 / \ 3 / 7 / 37 2*I*\/ 6267 61
- + ----------------------------------------------- + I*|----------------------------------------------- - ---------------------------- - -----------------------------| - ---------------------------- + ----------------------------- + - + ----------------------------------------------- + I*|----------------------------------------------- - ---------------------------- + -----------------------------| - ---------------------------- - ----------------------------- + - + 3 / -- + ------------ + --------------------------
3 9 \ 9 6 6 / 6 6 3 9 \ 9 6 6 / 6 6 3 \/ 27 9 ___________________
/ ______
/ 37 2*I*\/ 6267
9*3 / -- + ------------
\/ 27 9
$$\left(\frac{7}{3} + \frac{61}{9 \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}} + \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}\right) + \left(\left(- \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9} + \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{7}{3} + i \left(- \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9}\right)\right) + \left(\frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9} - \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} - \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{7}{3} + i \left(\frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6}\right)\right)\right)$$
=
/ 1 \ / 1 \ / / 1 \ \ / / 1 \ \
61*re|----------------------------------------| 61*re|----------------------------------------| |61*im|----------------------------------------| / / ______\\ / / ______\\| |61*im|----------------------------------------| / / ______\\ / / ______\\| / / ______\\
| ___________________| | ___________________| | | ___________________| | |6*\/ 6267 || | |6*\/ 6267 ||| | | ___________________| | |6*\/ 6267 || | |6*\/ 6267 ||| | |6*\/ 6267 ||
|/ ___\ / ______ | |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------||
___________________ || 1 I*\/ 3 | / 37 2*I*\/ 6267 | || 1 I*\/ 3 | / 37 2*I*\/ 6267 | | || 1 I*\/ 3 | / 37 2*I*\/ 6267 | ____ | \ 37 /| _____ | \ 37 /|| | || 1 I*\/ 3 | / 37 2*I*\/ 6267 | ____ | \ 37 /| _____ | \ 37 /|| ____ | \ 37 /|
/ ______ ||- - + -------|*3 / -- + ------------ | ||- - - -------|*3 / -- + ------------ | | ||- - + -------|*3 / -- + ------------ | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| | ||- - - -------|*3 / -- + ------------ | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| \/ 61 *cos|----------------|
/ 37 2*I*\/ 6267 61 \\ 2 2 / \/ 27 9 / \\ 2 2 / \/ 27 9 / | \\ 2 2 / \/ 27 9 / \ 3 / \ 3 /| | \\ 2 2 / \/ 27 9 / \ 3 / \ 3 /| \ 3 /
7 + 3 / -- + ------------ + -------------------------- + ----------------------------------------------- + ----------------------------------------------- + I*|----------------------------------------------- - ---------------------------- + -----------------------------| + I*|----------------------------------------------- - ---------------------------- - -----------------------------| - ----------------------------
\/ 27 9 ___________________ 9 9 \ 9 6 6 / \ 9 6 6 / 3
/ ______
/ 37 2*I*\/ 6267
9*3 / -- + ------------
\/ 27 9
$$- \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{3} + \frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9} + \frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9} + 7 + \frac{61}{9 \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}} + i \left(\frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6}\right) + i \left(- \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9}\right) + \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}$$
product
/ / 1 \ / / 1 \ \ \ / / 1 \ / / 1 \ \ \
| 61*re|----------------------------------------| |61*im|----------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\| | 61*re|----------------------------------------| |61*im|----------------------------------------| / / ______\\ / / ______\\| / / ______\\ / / ______\\|
| | ___________________| | | ___________________| | |6*\/ 6267 || | |6*\/ 6267 ||| | |6*\/ 6267 || | |6*\/ 6267 ||| | | ___________________| | | ___________________| | |6*\/ 6267 || | |6*\/ 6267 ||| | |6*\/ 6267 || | |6*\/ 6267 |||
| |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------||| | |/ ___\ / ______ | | |/ ___\ / ______ | |atan|----------|| |atan|----------||| |atan|----------|| |atan|----------|||
| || 1 I*\/ 3 | / 37 2*I*\/ 6267 | | || 1 I*\/ 3 | / 37 2*I*\/ 6267 | ____ | \ 37 /| _____ | \ 37 /|| ____ | \ 37 /| _____ | \ 37 /|| | || 1 I*\/ 3 | / 37 2*I*\/ 6267 | | || 1 I*\/ 3 | / 37 2*I*\/ 6267 | ____ | \ 37 /| _____ | \ 37 /|| ____ | \ 37 /| _____ | \ 37 /|| / ___________________ \
| ||- - - -------|*3 / -- + ------------ | | ||- - - -------|*3 / -- + ------------ | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| \/ 61 *cos|----------------| \/ 183 *sin|----------------|| | ||- - + -------|*3 / -- + ------------ | | ||- - + -------|*3 / -- + ------------ | \/ 61 *sin|----------------| \/ 183 *cos|----------------|| \/ 61 *cos|----------------| \/ 183 *sin|----------------|| | / ______ |
|7 \\ 2 2 / \/ 27 9 / | \\ 2 2 / \/ 27 9 / \ 3 / \ 3 /| \ 3 / \ 3 /| |7 \\ 2 2 / \/ 27 9 / | \\ 2 2 / \/ 27 9 / \ 3 / \ 3 /| \ 3 / \ 3 /| |7 / 37 2*I*\/ 6267 61 |
|- + ----------------------------------------------- + I*|----------------------------------------------- - ---------------------------- - -----------------------------| - ---------------------------- + -----------------------------|*|- + ----------------------------------------------- + I*|----------------------------------------------- - ---------------------------- + -----------------------------| - ---------------------------- - -----------------------------|*|- + 3 / -- + ------------ + --------------------------|
\3 9 \ 9 6 6 / 6 6 / \3 9 \ 9 6 6 / 6 6 / |3 \/ 27 9 ___________________|
| / ______ |
| / 37 2*I*\/ 6267 |
| 9*3 / -- + ------------ |
\ \/ 27 9 /
$$\left(- \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9} + \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{7}{3} + i \left(- \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} - \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9}\right)\right) \left(\frac{61 \operatorname{re}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9} - \frac{\sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} - \frac{\sqrt{183} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{7}{3} + i \left(\frac{61 \operatorname{im}{\left(\frac{1}{\left(- \frac{1}{2} + \frac{\sqrt{3} i}{2}\right) \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}}\right)}}{9} - \frac{\sqrt{61} \sin{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6} + \frac{\sqrt{183} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}}{6}\right)\right) \left(\frac{7}{3} + \frac{61}{9 \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}} + \sqrt[3]{\frac{37}{27} + \frac{2 \sqrt{6267} i}{9}}\right)$$
=
/ / / ______\\ / / ______\\\
| | |6*\/ 6267 || | |6*\/ 6267 |||
/ ___________________ / ___________________\\ | |2*atan|----------|| |atan|----------|||
| 3 / ______ | 3 / ______ || | | \ 37 /| ____ | \ 37 /||
\61 + \/ 37 + 6*I*\/ 6267 *\7 + \/ 37 + 6*I*\/ 6267 //*|-12 + 122*cos|------------------| - 14*\/ 61 *cos|----------------||
\ \ 3 / \ 3 //
--------------------------------------------------------------------------------------------------------------------------------
___________________
3 / ______
27*\/ 37 + 6*I*\/ 6267
$$\frac{\left(61 + \left(7 + \sqrt[3]{37 + 6 \sqrt{6267} i}\right) \sqrt[3]{37 + 6 \sqrt{6267} i}\right) \left(- 14 \sqrt{61} \cos{\left(\frac{\operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)} - 12 + 122 \cos{\left(\frac{2 \operatorname{atan}{\left(\frac{6 \sqrt{6267}}{37} \right)}}{3} \right)}\right)}{27 \sqrt[3]{37 + 6 \sqrt{6267} i}}$$
(61 + (37 + 6*i*sqrt(6267))^(1/3)*(7 + (37 + 6*i*sqrt(6267))^(1/3)))*(-12 + 122*cos(2*atan(6*sqrt(6267)/37)/3) - 14*sqrt(61)*cos(atan(6*sqrt(6267)/37)/3))/(27*(37 + 6*i*sqrt(6267))^(1/3))
Numerical answer
[src]
x1 = -2.10694687597486
x2 = 6.90852483455032
x3 = 2.19842204142454
x3 = 2.19842204142454