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^2-120P+P=0

We add all the numbers together, and all the variables

15P^2-119P=0

a = 15; b = -119; c = 0;
Δ = b2-4ac
Δ = -1192-4·15·0
Δ = 14161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14161}=119$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-119)-119}{2*15}=\frac{0}{30}
=0
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+119}{2*15}=\frac{238}{30}
=7+14/15
$