P(x)=0.04x^2+240x-1000

Solution for P(x)=0.04x^2+240x-1000 equation:

(P)=0.04P^2+240P-1000

We move all terms to the left:

(P)-(0.04P^2+240P-1000)=0

We get rid of parentheses

-0.04P^2+P-240P+1000=0

We add all the numbers together, and all the variables

-0.04P^2-239P+1000=0

a = -0.04; b = -239; c = +1000;
Δ = b2-4ac
Δ = -2392-4·(-0.04)·1000
Δ = 57281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{57281}=\sqrt{49*1169}=\sqrt{49}*\sqrt{1169}=7\sqrt{1169}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-239)-7\sqrt{1169}}{2*-0.04}=\frac{239-7\sqrt{1169}}{-0.08}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-239)+7\sqrt{1169}}{2*-0.04}=\frac{239+7\sqrt{1169}}{-0.08}
$