$$x^4-12x^3+48x^2-192+512 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.6128+2.25167i & x_2 = -0.6128-2.25167i & x_3 = 6.6128+3.87745i \\[1 em] x_4 = 6.6128-3.87745i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^4-12x^3+48x^2-192+512 &= 0&& \text{simplify left side} \\[1 em]x^4-12x^3+48x^2+320 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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