Y=3(x+6)(4x-2)

Solution for Y=3(x+6)(4x-2) equation:

=3(Y+6)(4Y-2)

We move all terms to the left:

-(3(Y+6)(4Y-2))=0

We multiply parentheses ..

-(3(+4Y^2-2Y+24Y-12))=0


We calculate terms in parentheses: -(3(+4Y^2-2Y+24Y-12)), so:

3(+4Y^2-2Y+24Y-12)

We multiply parentheses

12Y^2-6Y+72Y-36

We add all the numbers together, and all the variables

12Y^2+66Y-36

Back to the equation:

-(12Y^2+66Y-36)


We get rid of parentheses

-12Y^2-66Y+36=0

a = -12; b = -66; c = +36;
Δ = b2-4ac
Δ = -662-4·(-12)·36
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-78}{2*-12}=\frac{-12}{-24}
=1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+78}{2*-12}=\frac{144}{-24}
=-6
$