P=-20x^2+1000x-6720

Solution for P=-20x^2+1000x-6720 equation:

=-20P^2+1000P-6720

We move all terms to the left:

-(-20P^2+1000P-6720)=0

We get rid of parentheses

20P^2-1000P+6720=0

a = 20; b = -1000; c = +6720;
Δ = b2-4ac
Δ = -10002-4·20·6720
Δ = 462400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{462400}=680$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-680}{2*20}=\frac{320}{40}
=8
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+680}{2*20}=\frac{1680}{40}
=42
$