P(x)=-0.2x^2+24x-60

Solution for P(x)=-0.2x^2+24x-60 equation:

(P)=-0.2P^2+24P-60

We move all terms to the left:

(P)-(-0.2P^2+24P-60)=0

We get rid of parentheses

0.2P^2-24P+P+60=0

We add all the numbers together, and all the variables

0.2P^2-23P+60=0

a = 0.2; b = -23; c = +60;
Δ = b2-4ac
Δ = -232-4·0.2·60
Δ = 481
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{-(-23)-\sqrt{481}}{2*0.2}=\frac{23-\sqrt{481}}{0.4}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{481}}{2*0.2}=\frac{23+\sqrt{481}}{0.4}
$