$$x^4-3 = x$$
Answer
$$ \begin{matrix}x_1 = 1.45263 & x_2 = -1.16404 & x_3 = -0.1443+1.32415i \\[1 em] x_4 = -0.1443-1.32415i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^4-3 &= x&& \text{move all terms to the left hand side } \\[1 em]x^4-3-x &= 0&& \text{simplify left side} \\[1 em]x^4-x-3 &= 0&& \\[1 em] \end{aligned} $$
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