$$12x^5-26x^4+16x^3-10x^2+20x-10 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.65856 & x_2 = -0.42817+0.79665i & x_3 = -0.42817-0.79665i \\[1 em] x_4 = 1.18223+0.38641i & x_5 = 1.18223-0.38641i \\[1 em] \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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