P=-80p^2+2560p-17600

Solution for P=-80p^2+2560p-17600 equation:

=-80P^2+2560P-17600

We move all terms to the left:

-(-80P^2+2560P-17600)=0

We get rid of parentheses

80P^2-2560P+17600=0

a = 80; b = -2560; c = +17600;
Δ = b2-4ac
Δ = -25602-4·80·17600
Δ = 921600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{921600}=960$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2560)-960}{2*80}=\frac{1600}{160}
=10
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2560)+960}{2*80}=\frac{3520}{160}
=22
$