Y=2(x-6)(x+2)

Solution for Y=2(x-6)(x+2) equation:

=2(Y-6)(Y+2)

We move all terms to the left:

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

We multiply parentheses ..

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


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

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

We multiply parentheses

2Y^2+4Y-12Y-24

We add all the numbers together, and all the variables

2Y^2-8Y-24

Back to the equation:

-(2Y^2-8Y-24)


We get rid of parentheses

-2Y^2+8Y+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:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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