$$8x^7+7x^6+6x^5+5x^4+4x^3+3x^2+2x+1 = 0$$
Answer
$$ \begin{matrix}x_1 = -0.71454 & x_2 = -0.52742+0.49067i & x_3 = -0.52742-0.49067i \\[1 em] x_4 = -0.05179+0.73825i & x_5 = -0.05179-0.73825i & x_6 = 0.49898+0.60542i \\[1 em] x_7 = 0.49898-0.60542i & \\[1 em] \end{matrix} $$
Explanation
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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Polynomial Equations Solver