$$11x^3-x^5-11x^2 = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 1.1318 & x_3 = 2.60258 \\[1 em] x_4 = -3.73438 & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 11x^3-x^5-11x^2 &= 0&& \text{simplify left side} \\[1 em]-x^5+11x^3-11x^2 &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -x^{5}+11x^{3}-11x^{2} = 0 } $, first we need to factor our $ x^2 $.
$$ -x^{5}+11x^{3}-11x^{2} = x^2 \left( -x^{3}+11x-11 \right) $$$ x = 0 $ is a root of multiplicity $ 2 $.
The remaining roots can be found by solving equation $ -x^{3}+11x-11 = 0$.
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