P(x)=20x-0.002x^2

Solution for P(x)=20x-0.002x^2 equation:

(P)=20P-0.002P^2

We move all terms to the left:

(P)-(20P-0.002P^2)=0

We get rid of parentheses

0.002P^2-20P+P=0

We add all the numbers together, and all the variables

0.002P^2-19P=0

a = 0.002; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·0.002·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*0.002}=\frac{0}{0.004}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*0.002}=\frac{38}{0.004}
=9500
$