$$x^5+3x^5-4x\cdot2+10 = x+2$$
Answer
$$ \begin{matrix}x_1 = -1.38624 & x_2 = 0.87281+0.29417i & x_3 = 0.87281-0.29417i \\[1 em] x_4 = -0.1797+1.29166i & x_5 = -0.1797-1.29166i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^5+3x^5-4x\cdot2+10 &= x+2&& \text{simplify left side} \\[1 em]x^5+3x^5-8x+10 &= x+2&& \\[1 em]4x^5-8x+10 &= x+2&& \text{move all terms to the left hand side } \\[1 em]4x^5-8x+10-x-2 &= 0&& \text{simplify left side} \\[1 em]4x^5-9x+8 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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