P(x)=-x^2+40x-100

Solution for P(x)=-x^2+40x-100 equation:

(P)=-P^2+40P-100

We move all terms to the left:

(P)-(-P^2+40P-100)=0

We get rid of parentheses

P^2-40P+P+100=0

We add all the numbers together, and all the variables

P^2-39P+100=0

a = 1; b = -39; c = +100;
Δ = b2-4ac
Δ = -392-4·1·100
Δ = 1121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-\sqrt{1121}}{2*1}=\frac{39-\sqrt{1121}}{2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1121}}{2*1}=\frac{39+\sqrt{1121}}{2}
$