P(c)=-12c^2+120

Solution for P(c)=-12c^2+120 equation:

(P)=-12P^2+120

We move all terms to the left:

(P)-(-12P^2+120)=0

We get rid of parentheses

12P^2+P-120=0

a = 12; b = 1; c = -120;
Δ = b2-4ac
Δ = 12-4·12·(-120)
Δ = 5761
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{-(1)-\sqrt{5761}}{2*12}=\frac{-1-\sqrt{5761}}{24}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{5761}}{2*12}=\frac{-1+\sqrt{5761}}{24}
$