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$$6x^6+x^5-5x^4+2x^3+x^2+x+6 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.94698+0.51863i & x_2 = 0.94698-0.51863i & x_3 = -0.00176+0.86315i \\[1 em] x_4 = -0.00176-0.86315i & x_5 = -1.02855+0.30575i & x_6 = -1.02855-0.30575i \end{matrix} $$
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