$$(3x^2+2)(x^2+3) = 0$$
Answer
$$ \begin{matrix}x_1 = 0.8165i & x_2 = -0.8165i & x_3 = 1.73205i \\[1 em] x_4 = -1.73205i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (3x^2+2)(x^2+3) &= 0&& \text{simplify left side} \\[1 em]3x^4+9x^2+2x^2+6 &= 0&& \\[1 em]3x^4+11x^2+6 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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