$$x^4+10x^3+36x^2+55x+18 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.43845 & x_2 = -4.56155 & x_3 = -2.5+1.65831i \\[1 em] x_4 = -2.5-1.65831i & \\[1 em] \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
This page was created using
Polynomial Equations Solver