$$7x^6-20x^4+12x^2 = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 0.92582 & x_3 = -0.92582 \\[1 em] x_4 = 1.41421 & x_5 = -1.41421 \\[1 em] \end{matrix} $$
Explanation
In order to solve $ \color{blue}{ 7x^{6}-20x^{4}+12x^{2} = 0 } $, first we need to factor our $ x^2 $.
$$ 7x^{6}-20x^{4}+12x^{2} = x^2 \left( 7x^{4}-20x^{2}+12 \right) $$$ x = 0 $ is a root of multiplicity $ 2 $.
The remaining roots can be found by solving equation $ 7x^{4}-20x^{2}+12 = 0$.
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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