P(x)=-0.002x^2+30x+500000

Solution for P(x)=-0.002x^2+30x+500000 equation:

(P)=-0.002P^2+30P+500000

We move all terms to the left:

(P)-(-0.002P^2+30P+500000)=0

We get rid of parentheses

0.002P^2-30P+P-500000=0

We add all the numbers together, and all the variables

0.002P^2-29P-500000=0

a = 0.002; b = -29; c = -500000;
Δ = b2-4ac
Δ = -292-4·0.002·(-500000)
Δ = 4841
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{-(-29)-\sqrt{4841}}{2*0.002}=\frac{29-\sqrt{4841}}{0.004}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{4841}}{2*0.002}=\frac{29+\sqrt{4841}}{0.004}
$