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$$2x^5+5x^4+10x^3+10x^2+10x+10 = 0$$
Answer
$$ \begin{matrix}x_1 = -1.23206 & x_2 = 0.26415+1.12073i & x_3 = 0.26415-1.12073i \\[1 em] x_4 = -0.89811+1.50144i & x_5 = -0.89811-1.50144i \\[1 em] \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
This page was created using
Polynomial Equations Solver