$$(x^2-2x+3)(x^2-2x-2) = 0$$
Answer
$$ \begin{matrix}x_1 = -0.73205 & x_2 = 2.73205 & x_3 = 1+1.41421i \\[1 em] x_4 = 1-1.41421i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (x^2-2x+3)(x^2-2x-2) &= 0&& \text{simplify left side} \\[1 em]x^4-4x^3+5x^2-2x-6 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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