The roots of polynomial $ p(x) $ are:
$$ \begin{aligned}x_1 &= -0.2846\\[1 em]x_2 &= -49999.7154 \end{aligned} $$The solutions of $ x^2+50000x+14231 = 0 $ are: $ x = -25000-\sqrt{ 624985769 } ~ \text{and} ~ x = -25000+\sqrt{ 624985769 }$.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this quadratic equation.