P(x)=-2x^2+38x-120

Solution for P(x)=-2x^2+38x-120 equation:

(P)=-2P^2+38P-120

We move all terms to the left:

(P)-(-2P^2+38P-120)=0

We get rid of parentheses

2P^2-38P+P+120=0

We add all the numbers together, and all the variables

2P^2-37P+120=0

a = 2; b = -37; c = +120;
Δ = b2-4ac
Δ = -372-4·2·120
Δ = 409
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{-(-37)-\sqrt{409}}{2*2}=\frac{37-\sqrt{409}}{4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{409}}{2*2}=\frac{37+\sqrt{409}}{4}
$