$$3x^4-4x^2+5 = x$$
Answer
$$ \begin{matrix}x_1 = 0.99005+0.47892i & x_2 = 0.99005-0.47892i & x_3 = -0.99005+0.63064i \\[1 em] x_4 = -0.99005-0.63064i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 3x^4-4x^2+5 &= x&& \text{move all terms to the left hand side } \\[1 em]3x^4-4x^2+5-x &= 0&& \text{simplify left side} \\[1 em]3x^4-4x^2-x+5 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
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Polynomial Equations Solver