The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= 4.8778\\[1 em]x_2 &= -3.8378 \end{aligned} $$The solutions of $ 25x^2-26x-468 = 0 $ are: $ x = \dfrac{ 13 }{ 25 }-\dfrac{\sqrt{ 11869 }}{ 25 } ~ \text{and} ~ x = \dfrac{ 13 }{ 25 }+\dfrac{\sqrt{ 11869 }}{ 25 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.