The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -3.5106\\[1 em]x_2 &= 3.5106\\[1 em]x_3 &= 0.5697i\\[1 em]x_4 &= -0.5697i \end{aligned} $$Polynomial $ x^4-12x^2-4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.