$$4x^6+2x^5+x^3+x-1 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.56714 & x_2 = -1.07592 & x_3 = 0.41079+0.65898i \\[1 em] x_4 = 0.41079-0.65898i & x_5 = -0.4064+0.71713i & x_6 = -0.4064-0.71713i \end{matrix} $$
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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