$$878x^4+889x^3+1600x^2+121x+2 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.02412 & x_2 = -0.05402 & x_3 = -0.46719+1.23682i \\[1 em] x_4 = -0.46719-1.23682i & \\[1 em] \end{matrix} $$
Explanation
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