$$2x^4-18^2+3x^2-27 = 0$$
Answer
$$ \begin{matrix}x_1 = 3.5382 & x_2 = -3.5382 & x_3 = 3.74418i \\[1 em] x_4 = -3.74418i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 2x^4-18^2+3x^2-27 &= 0&& \text{simplify left side} \\[1 em]2x^4-324+3x^2-27 &= 0&& \\[1 em]2x^4+3x^2-351 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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