$$-5x^6-6x^2+6x^5+4 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.9029 & x_2 = -0.67243 & x_3 = -0.49696+0.84083i \\[1 em] x_4 = -0.49696-0.84083i & x_5 = 0.98173+0.64611i & x_6 = 0.98173-0.64611i \end{matrix} $$
Explanation
$$ \begin{aligned} -5x^6-6x^2+6x^5+4 &= 0&& \text{simplify left side} \\[1 em]-5x^6+6x^5-6x^2+4 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
This page was created using
Polynomial Equations Solver