$$3+12x-9x^4-20x^5+4x^8 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.24872 & x_2 = -0.904 & x_3 = 0.86338 \\[1 em] x_4 = 1.80951 & x_5 = -0.01962+0.87643i & x_6 = -0.01962-0.87643i \\[1 em] x_7 = -0.74046+1.4933i & x_8 = -0.74046-1.4933i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 3+12x-9x^4-20x^5+4x^8 &= 0&& \text{simplify left side} \\[1 em]4x^8-20x^5-9x^4+12x+3 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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