P(x)=110x-x2-1000

Solution for P(x)=110x-x2-1000 equation:

(P)=110P-P2-1000

We move all terms to the left:

(P)-(110P-P2-1000)=0

We add all the numbers together, and all the variables

-(+110P-1P^2-1000)+P=0

We get rid of parentheses

1P^2-110P+P+1000=0

We add all the numbers together, and all the variables

P^2-109P+1000=0

a = 1; b = -109; c = +1000;
Δ = b2-4ac
Δ = -1092-4·1·1000
Δ = 7881
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{-(-109)-\sqrt{7881}}{2*1}=\frac{109-\sqrt{7881}}{2}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-109)+\sqrt{7881}}{2*1}=\frac{109+\sqrt{7881}}{2}
$