P(x)=-12x^2+1320x-21600

Solution for P(x)=-12x^2+1320x-21600 equation:

(P)=-12P^2+1320P-21600

We move all terms to the left:

(P)-(-12P^2+1320P-21600)=0

We get rid of parentheses

12P^2-1320P+P+21600=0

We add all the numbers together, and all the variables

12P^2-1319P+21600=0

a = 12; b = -1319; c = +21600;
Δ = b2-4ac
Δ = -13192-4·12·21600
Δ = 702961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1319)-\sqrt{702961}}{2*12}=\frac{1319-\sqrt{702961}}{24}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1319)+\sqrt{702961}}{2*12}=\frac{1319+\sqrt{702961}}{24}
$