P=-x^2+130x-3000

Solution for P=-x^2+130x-3000 equation:

=-P^2+130P-3000

We move all terms to the left:

-(-P^2+130P-3000)=0

We get rid of parentheses

P^2-130P+3000=0

a = 1; b = -130; c = +3000;
Δ = b2-4ac
Δ = -1302-4·1·3000
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-70}{2*1}=\frac{60}{2}
=30
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+70}{2*1}=\frac{200}{2}
=100
$