The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 0.9343\\[1 em]x_2 &= -0.2676 \end{aligned} $$The solutions of $ -12x^2+8x+3 = 0 $ are: $ x = \dfrac{ 1 }{ 3 }-\dfrac{\sqrt{ 13 }}{ 6 } ~ \text{and} ~ x = \dfrac{ 1 }{ 3 }+\dfrac{\sqrt{ 13 }}{ 6 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.