The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 1.2626\\[1 em]x_2 &= -0.6313+0.4422i\\[1 em]x_3 &= -0.6313-0.4422i \end{aligned} $$Polynomial $ 4x^3-4x-3 $ has no rational roots that can be found using Rational Root Test, so the roots were found using qubic formulas.