P=-15x^2+240x-640

Solution for P=-15x^2+240x-640 equation:

=-15P^2+240P-640

We move all terms to the left:

-(-15P^2+240P-640)=0

We get rid of parentheses

15P^2-240P+640=0

a = 15; b = -240; c = +640;
Δ = b2-4ac
Δ = -2402-4·15·640
Δ = 19200
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:

$\sqrt{\Delta}=\sqrt{19200}=\sqrt{6400*3}=\sqrt{6400}*\sqrt{3}=80\sqrt{3}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-80\sqrt{3}}{2*15}=\frac{240-80\sqrt{3}}{30}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+80\sqrt{3}}{2*15}=\frac{240+80\sqrt{3}}{30}
$