$$x^4+10x^3+37x^2+78x+10 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.13675 & x_2 = -5.93105 & x_3 = -1.9661+2.90922i \\[1 em] x_4 = -1.9661-2.90922i & \\[1 em] \end{matrix} $$
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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