$$y^8+4y^7+18y^6+40y^5+91y^4+119y^3+167y^2+111y+99 = 0$$
Answer
$$ \begin{matrix}y_1 = 0.03371+1.41407i & y_2 = 0.03371-1.41407i & y_3 = -0.5+1.65831i \\[1 em] y_4 = -0.5-1.65831i & y_5 = -0.45286+2.15316i & y_6 = -0.45286-2.15316i \\[1 em] y_7 = -1.08085+1.49625i & y_8 = -1.08085-1.49625i \\[1 em] \end{matrix} $$
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