$$(x^2-8)(3x^2+8) = 0$$
Answer
$$ \begin{matrix}x_1 = 2.82843 & x_2 = -2.82843 & x_3 = 1.63299i \\[1 em] x_4 = -1.63299i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (x^2-8)(3x^2+8) &= 0&& \text{simplify left side} \\[1 em]3x^4+8x^2-24x^2-64 &= 0&& \\[1 em]3x^4-16x^2-64 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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