$$-5x^5+9x^4+7x^2+6x^2 = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 2.29405 & x_3 = -0.24702+1.03554i \\[1 em] x_4 = -0.24702-1.03554i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} -5x^5+9x^4+7x^2+6x^2 &= 0&& \text{simplify left side} \\[1 em]-5x^5+9x^4+13x^2 &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -5x^{5}+9x^{4}+13x^{2} = 0 } $, first we need to factor our $ x^2 $.
$$ -5x^{5}+9x^{4}+13x^{2} = x^2 \left( -5x^{3}+9x^{2}+13 \right) $$$ x = 0 $ is a root of multiplicity $ 2 $.
The remaining roots can be found by solving equation $ -5x^{3}+9x^{2}+13 = 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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