P(x)=200x-0.2x^2-7500

Solution for P(x)=200x-0.2x^2-7500 equation:

(P)=200P-0.2P^2-7500

We move all terms to the left:

(P)-(200P-0.2P^2-7500)=0

We get rid of parentheses

0.2P^2-200P+P+7500=0

We add all the numbers together, and all the variables

0.2P^2-199P+7500=0

a = 0.2; b = -199; c = +7500;
Δ = b2-4ac
Δ = -1992-4·0.2·7500
Δ = 33601
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{-(-199)-\sqrt{33601}}{2*0.2}=\frac{199-\sqrt{33601}}{0.4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-199)+\sqrt{33601}}{2*0.2}=\frac{199+\sqrt{33601}}{0.4}
$