P=-x^2+130x-2200

Solution for P=-x^2+130x-2200 equation:

=-P^2+130P-2200

We move all terms to the left:

-(-P^2+130P-2200)=0

We get rid of parentheses

P^2-130P+2200=0

a = 1; b = -130; c = +2200;
Δ = b2-4ac
Δ = -1302-4·1·2200
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-90}{2*1}=\frac{40}{2}
=20
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+90}{2*1}=\frac{220}{2}
=110
$