$$x^3-9x^2+22x-13 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.87158 & x_2 = 2.79836 & x_3 = 5.33006 \end{matrix} $$
Explanation
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