P^2-25p=50-2p^2

Solution for P^2-25p=50-2p^2 equation:

^2-25P=50-2P^2

We move all terms to the left:

^2-25P-(50-2P^2)=0

We add all the numbers together, and all the variables

-(50-2P^2)-25P=0

We get rid of parentheses

2P^2-25P-50=0

a = 2; b = -25; c = -50;
Δ = b2-4ac
Δ = -252-4·2·(-50)
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{41}}{2*2}=\frac{25-5\sqrt{41}}{4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{41}}{2*2}=\frac{25+5\sqrt{41}}{4}
$