P=-x^2+48x-512

Solution for P=-x^2+48x-512 equation:

=-P^2+48P-512

We move all terms to the left:

-(-P^2+48P-512)=0

We get rid of parentheses

P^2-48P+512=0

a = 1; b = -48; c = +512;
Δ = b2-4ac
Δ = -482-4·1·512
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-16}{2*1}=\frac{32}{2}
=16
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+16}{2*1}=\frac{64}{2}
=32
$