P(x)=120x-x^2-1100

Solution for P(x)=120x-x^2-1100 equation:

(P)=120P-P^2-1100

We move all terms to the left:

(P)-(120P-P^2-1100)=0

We get rid of parentheses

P^2-120P+P+1100=0

We add all the numbers together, and all the variables

P^2-119P+1100=0

a = 1; b = -119; c = +1100;
Δ = b2-4ac
Δ = -1192-4·1·1100
Δ = 9761
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{-(-119)-\sqrt{9761}}{2*1}=\frac{119-\sqrt{9761}}{2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+\sqrt{9761}}{2*1}=\frac{119+\sqrt{9761}}{2}
$