$$1+x-x^3 = 0$$
Answer
$$ \begin{matrix}x_1 = 1.32472 & x_2 = -0.66236+0.56228i & x_3 = -0.66236-0.56228i \end{matrix} $$
Explanation
$$ \begin{aligned} 1+x-x^3 &= 0&& \text{simplify left side} \\[1 em]-x^3+x+1 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Polynomial Equations Solver