P(c)=15c(c-8)

Solution for P(c)=15c(c-8) equation:

(P)=15P(P-8)

We move all terms to the left:

(P)-(15P(P-8))=0


We calculate terms in parentheses: -(15P(P-8)), so:

15P(P-8)

We multiply parentheses

15P^2-120P

Back to the equation:

-(15P^2-120P)


We get rid of parentheses

-15P^2+P+120P=0

We add all the numbers together, and all the variables

-15P^2+121P=0

a = -15; b = 121; c = 0;
Δ = b2-4ac
Δ = 1212-4·(-15)·0
Δ = 14641
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14641}=121$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(121)-121}{2*-15}=\frac{-242}{-30}
=8+1/15
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(121)+121}{2*-15}=\frac{0}{-30}
=0
$