P(x)=-2x2+500x+20,

Solution for P(x)=-2x2+500x+20, equation:

(P)=-2P^2+500P+20.

We move all terms to the left:

(P)-(-2P^2+500P+20.)=0

We get rid of parentheses

2P^2-500P+P-20.=0

We add all the numbers together, and all the variables

2P^2-499P-20=0

a = 2; b = -499; c = -20;
Δ = b2-4ac
Δ = -4992-4·2·(-20)
Δ = 249161
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{-(-499)-\sqrt{249161}}{2*2}=\frac{499-\sqrt{249161}}{4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-499)+\sqrt{249161}}{2*2}=\frac{499+\sqrt{249161}}{4}
$