P(x)=500+100x-5x^2

Solution for P(x)=500+100x-5x^2 equation:

(P)=500+100P-5P^2

We move all terms to the left:

(P)-(500+100P-5P^2)=0

We get rid of parentheses

5P^2-100P+P-500=0

We add all the numbers together, and all the variables

5P^2-99P-500=0

a = 5; b = -99; c = -500;
Δ = b2-4ac
Δ = -992-4·5·(-500)
Δ = 19801
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{-(-99)-\sqrt{19801}}{2*5}=\frac{99-\sqrt{19801}}{10}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+\sqrt{19801}}{2*5}=\frac{99+\sqrt{19801}}{10}
$