$$x^7+4x^5+6x^3+30x-560 = 0$$
Answer
$$ \begin{matrix}x_1 = 2.18114 & x_2 = 1.41838+2.07614i & x_3 = 1.41838-2.07614i \\[1 em] x_4 = -2.03956+1.21671i & x_5 = -2.03956-1.21671i & x_6 = -0.46939+2.64195i \\[1 em] x_7 = -0.46939-2.64195i & \\[1 em] \end{matrix} $$
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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