$$18x^6 = 3x^2$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = 0.63894 & x_3 = -0.63894 \\[1 em] x_4 = 0.63894i & x_5 = -0.63894i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 18x^6 &= 3x^2&& \text{move all terms to the left hand side } \\[1 em]18x^6-3x^2 &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 18x^{6}-3x^{2} = 0 } $, first we need to factor our $ x^2 $.
$$ 18x^{6}-3x^{2} = x^2 \left( 18x^{4}-3 \right) $$$ x = 0 $ is a root of multiplicity $ 2 $.
The remaining roots can be found by solving equation $ 18x^{4}-3 = 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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