P(x)=3(x-2)(2x+4)

Solution for P(x)=3(x-2)(2x+4) equation:

(P)=3(P-2)(2P+4)

We move all terms to the left:

(P)-(3(P-2)(2P+4))=0

We multiply parentheses ..

-(3(+2P^2+4P-4P-8))+P=0


We calculate terms in parentheses: -(3(+2P^2+4P-4P-8)), so:

3(+2P^2+4P-4P-8)

We multiply parentheses

6P^2+12P-12P-24

We add all the numbers together, and all the variables

6P^2-24

Back to the equation:

-(6P^2-24)


We add all the numbers together, and all the variables

P-(6P^2-24)=0

We get rid of parentheses

-6P^2+P+24=0

a = -6; b = 1; c = +24;
Δ = b2-4ac
Δ = 12-4·(-6)·24
Δ = 577
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{-(1)-\sqrt{577}}{2*-6}=\frac{-1-\sqrt{577}}{-12}
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{577}}{2*-6}=\frac{-1+\sqrt{577}}{-12}
$