Y=2x(6x-12)

Solution for Y=2x(6x-12) equation:

=2Y(6Y-12)

We move all terms to the left:

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


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

2Y(6Y-12)

We multiply parentheses

12Y^2-24Y

Back to the equation:

-(12Y^2-24Y)


We get rid of parentheses

-12Y^2+24Y=0

a = -12; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-12)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-12}=\frac{-48}{-24}
=+2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-12}=\frac{0}{-24}
=0
$