$$x^3 = 1-2x$$
Answer
$$ \begin{matrix}x_1 = 0.4534 & x_2 = -0.2267+1.46771i & x_3 = -0.2267-1.46771i \end{matrix} $$
Explanation
$$ \begin{aligned} x^3 &= 1-2x&& \text{move all terms to the left hand side } \\[1 em]x^3-1+2x &= 0&& \text{simplify left side} \\[1 em]x^3+2x-1 &= 0&& \\[1 em] \end{aligned} $$
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