Question
$$x^4-10x^2+258 = x$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x^4-10x^2+258 &= x&& \text{move all terms to the left hand side } \\[1 em]x^4-10x^2+258-x &= 0&& \text{simplify left side} \\[1 em]x^4-10x^2-x+258 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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