$$0 = x^3+5x-8$$
Answer
$$ \begin{matrix}x_1 = 1.22886 & x_2 = -0.61443+2.4764i & x_3 = -0.61443-2.4764i \end{matrix} $$
Explanation
$$ \begin{aligned} 0 &= x^3+5x-8&& \text{move all terms to the left hand side } \\[1 em]0-x^3-5x+8 &= 0&& \text{simplify left side} \\[1 em]-x^3-5x+8 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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