$$1+x^4+7x-7x^3+8x^2 = x+6$$
Answer
$$ \begin{matrix}x_1 = 0.58907 & x_2 = -0.82965 & x_3 = 1.92447 \\[1 em] x_4 = 5.31612 & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 1+x^4+7x-7x^3+8x^2 &= x+6&& \text{simplify left side} \\[1 em]x^4-7x^3+8x^2+7x+1 &= x+6&& \text{move all terms to the left hand side } \\[1 em]x^4-7x^3+8x^2+7x+1-x-6 &= 0&& \text{simplify left side} \\[1 em]x^4-7x^3+8x^2+6x-5 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
This page was created using
Polynomial Equations Solver