P(x)=12x^2+240x-900

Solution for P(x)=12x^2+240x-900 equation:

(P)=12P^2+240P-900

We move all terms to the left:

(P)-(12P^2+240P-900)=0

We get rid of parentheses

-12P^2+P-240P+900=0

We add all the numbers together, and all the variables

-12P^2-239P+900=0

a = -12; b = -239; c = +900;
Δ = b2-4ac
Δ = -2392-4·(-12)·900
Δ = 100321
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{-(-239)-\sqrt{100321}}{2*-12}=\frac{239-\sqrt{100321}}{-24}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-239)+\sqrt{100321}}{2*-12}=\frac{239+\sqrt{100321}}{-24}
$