$$x^4-16x^2 = x^2+18$$
Answer
$$ \begin{matrix}x_1 = 4.24264 & x_2 = -4.24264 & x_3 = 1i \\[1 em] x_4 = -i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x^4-16x^2 &= x^2+18&& \text{move all terms to the left hand side } \\[1 em]x^4-16x^2-x^2-18 &= 0&& \text{simplify left side} \\[1 em]x^4-17x^2-18 &= 0&& \\[1 em] \end{aligned} $$
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