2p^2-20p=50

Solution for 2p^2-20p=50 equation:

2p^2-20p=50

We move all terms to the left:

2p^2-20p-(50)=0

a = 2; b = -20; c = -50;
Δ = b2-4ac
Δ = -202-4·2·(-50)
Δ = 800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{2}}{2*2}=\frac{20-20\sqrt{2}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{2}}{2*2}=\frac{20+20\sqrt{2}}{4}
$