$$-10+2x+2x^2+3x^3+5x^4+6x^5+2x^6 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.82656 & x_2 = -2.22079 & x_3 = 0.29874+1.0877i \\[1 em] x_4 = 0.29874-1.0877i & x_5 = -1.10162+0.96296i & x_6 = -1.10162-0.96296i \end{matrix} $$
Explanation
$$ \begin{aligned} -10+2x+2x^2+3x^3+5x^4+6x^5+2x^6 &= 0&& \text{simplify left side} \\[1 em]2x^6+6x^5+5x^4+3x^3+2x^2+2x-10 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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