The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -1.5332\\[1 em]x_2 &= 1.5332\\[1 em]x_3 &= 0.9224i\\[1 em]x_4 &= -0.9224i \end{aligned} $$Polynomial $ -2x^4+3x^2+4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.