The roots of polynomial $ p(t) $ are:
$$ \begin{aligned}t_1 &= 3.3968\\[1 em]t_2 &= 0.2699 \end{aligned} $$The solutions of $ 12t^2-44t+11 = 0 $ are: $ t = \dfrac{ 11 }{ 6 }-\dfrac{\sqrt{ 22 }}{ 3 } ~ \text{and} ~ t = \dfrac{ 11 }{ 6 }+\dfrac{\sqrt{ 22 }}{ 3 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.