Y=12x^2+24x-135

Solution for Y=12x^2+24x-135 equation:

=12Y^2+24Y-135

We move all terms to the left:

-(12Y^2+24Y-135)=0

We get rid of parentheses

-12Y^2-24Y+135=0

a = -12; b = -24; c = +135;
Δ = b2-4ac
Δ = -242-4·(-12)·135
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-84}{2*-12}=\frac{-60}{-24}
=2+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+84}{2*-12}=\frac{108}{-24}
=-4+1/2
$