P(x)=-0.002x^2+150x+50000

Solution for P(x)=-0.002x^2+150x+50000 equation:

(P)=-0.002P^2+150P+50000

We move all terms to the left:

(P)-(-0.002P^2+150P+50000)=0

We get rid of parentheses

0.002P^2-150P+P-50000=0

We add all the numbers together, and all the variables

0.002P^2-149P-50000=0

a = 0.002; b = -149; c = -50000;
Δ = b2-4ac
Δ = -1492-4·0.002·(-50000)
Δ = 22601
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{-(-149)-\sqrt{22601}}{2*0.002}=\frac{149-\sqrt{22601}}{0.004}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-149)+\sqrt{22601}}{2*0.002}=\frac{149+\sqrt{22601}}{0.004}
$