$$4+9n^2+2n^2+5-4n^4+10n^2-6n^4 = 0$$
Answer
$$ \begin{matrix}n_1 = -1.57006 & n_2 = 1.57006 & n_3 = 0.60423i \\[1 em] n_4 = -0.60423i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 4+9n^2+2n^2+5-4n^4+10n^2-6n^4 &= 0&& \text{simplify left side} \\[1 em]-4n^4+11n^2+9+10n^2-6n^4 &= 0&& \\[1 em]-10n^4+21n^2+9 &= 0&& \\[1 em] \end{aligned} $$
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