$$(x^2-5x+2)(3x^2+2x+3) = 0$$
Answer
$$ \begin{matrix}x_1 = 0.43845 & x_2 = 4.56155 & x_3 = -0.33333+0.94281i \\[1 em] x_4 = -0.33333-0.94281i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (x^2-5x+2)(3x^2+2x+3) &= 0&& \text{simplify left side} \\[1 em]3x^4-13x^3-x^2-11x+6 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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Polynomial Equations Solver