P=-0.04x2+240x-10000

Solution for P=-0.04x2+240x-10000 equation:

=-0.04P^2+240P-10000

We move all terms to the left:

-(-0.04P^2+240P-10000)=0

We get rid of parentheses

0.04P^2-240P+10000=0

a = 0.04; b = -240; c = +10000;
Δ = b2-4ac
Δ = -2402-4·0.04·10000
Δ = 56000
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:

$\sqrt{\Delta}=\sqrt{56000}=\sqrt{1600*35}=\sqrt{1600}*\sqrt{35}=40\sqrt{35}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-40\sqrt{35}}{2*0.04}=\frac{240-40\sqrt{35}}{0.08}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+40\sqrt{35}}{2*0.04}=\frac{240+40\sqrt{35}}{0.08}
$