The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.9086\\[1 em]x_2 &= -0.4543+0.7868i\\[1 em]x_3 &= -0.4543-0.7868i \end{aligned} $$Polynomial $ 4x^3-3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.