P(s)=-24s^2+2200s-18000

Solution for P(s)=-24s^2+2200s-18000 equation:

(P)=-24P^2+2200P-18000

We move all terms to the left:

(P)-(-24P^2+2200P-18000)=0

We get rid of parentheses

24P^2-2200P+P+18000=0

We add all the numbers together, and all the variables

24P^2-2199P+18000=0

a = 24; b = -2199; c = +18000;
Δ = b2-4ac
Δ = -21992-4·24·18000
Δ = 3107601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3107601}=\sqrt{9*345289}=\sqrt{9}*\sqrt{345289}=3\sqrt{345289}$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2199)-3\sqrt{345289}}{2*24}=\frac{2199-3\sqrt{345289}}{48}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2199)+3\sqrt{345289}}{2*24}=\frac{2199+3\sqrt{345289}}{48}
$