The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.1283\\[1 em]x_2 &= -1.922\\[1 em]x_3 &= -0.6032+0.312i\\[1 em]x_4 &= -0.6032-0.312i \end{aligned} $$Polynomial $ 4x^4+8x^3-3x^2-9x-4 $ has no rational roots that can be found using Rational Root Test, so the roots were found using quartic formulas.