P=-6x^2+72x-192

Solution for P=-6x^2+72x-192 equation:

=-6P^2+72P-192

We move all terms to the left:

-(-6P^2+72P-192)=0

We get rid of parentheses

6P^2-72P+192=0

a = 6; b = -72; c = +192;
Δ = b2-4ac
Δ = -722-4·6·192
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-24}{2*6}=\frac{48}{12}
=4
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+24}{2*6}=\frac{96}{12}
=8
$