$$x^2+x^3 = 6$$
Answer
$$ \begin{matrix}x_1 = 1.53766 & x_2 = -1.26883+1.51397i & x_3 = -1.26883-1.51397i \end{matrix} $$
Explanation
$$ \begin{aligned} x^2+x^3 &= 6&& \text{simplify left side} \\[1 em]x^3+x^2 &= 6&& \text{move all terms to the left hand side } \\[1 em]x^3+x^2-6 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
This page was created using
Polynomial Equations Solver