P(x)=-5x^2+1000x+5000

Solution for P(x)=-5x^2+1000x+5000 equation:

(P)=-5P^2+1000P+5000

We move all terms to the left:

(P)-(-5P^2+1000P+5000)=0

We get rid of parentheses

5P^2-1000P+P-5000=0

We add all the numbers together, and all the variables

5P^2-999P-5000=0

a = 5; b = -999; c = -5000;
Δ = b2-4ac
Δ = -9992-4·5·(-5000)
Δ = 1098001
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{-(-999)-\sqrt{1098001}}{2*5}=\frac{999-\sqrt{1098001}}{10}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-999)+\sqrt{1098001}}{2*5}=\frac{999+\sqrt{1098001}}{10}
$