P=-2(n-6)(n+2)

Solution for P=-2(n-6)(n+2) equation:

=-2(P-6)(P+2)

We move all terms to the left:

-(-2(P-6)(P+2))=0

We multiply parentheses ..

-(-2(+P^2+2P-6P-12))=0


We calculate terms in parentheses: -(-2(+P^2+2P-6P-12)), so:

-2(+P^2+2P-6P-12)

We multiply parentheses

-2P^2-4P+12P+24

We add all the numbers together, and all the variables

-2P^2+8P+24

Back to the equation:

-(-2P^2+8P+24)


We get rid of parentheses

2P^2-8P-24=0

a = 2; b = -8; c = -24;
Δ = b2-4ac
Δ = -82-4·2·(-24)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16}{2*2}=\frac{-8}{4}
=-2
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16}{2*2}=\frac{24}{4}
=6
$