P=-0.04x2+240x-9000

Solution for P=-0.04x2+240x-9000 equation:

=-0.04P^2+240P-9000

We move all terms to the left:

-(-0.04P^2+240P-9000)=0

We get rid of parentheses

0.04P^2-240P+9000=0

a = 0.04; b = -240; c = +9000;
Δ = b2-4ac
Δ = -2402-4·0.04·9000
Δ = 56160
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:

$\sqrt{\Delta}=\sqrt{56160}=\sqrt{144*390}=\sqrt{144}*\sqrt{390}=12\sqrt{390}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-12\sqrt{390}}{2*0.04}=\frac{240-12\sqrt{390}}{0.08}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+12\sqrt{390}}{2*0.04}=\frac{240+12\sqrt{390}}{0.08}
$