Y=8x^2-12x

Solution for Y=8x^2-12x equation:

=8Y^2-12Y

We move all terms to the left:

-(8Y^2-12Y)=0

We get rid of parentheses

-8Y^2+12Y=0

a = -8; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-8)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-8}=\frac{-24}{-16}
=1+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-8}=\frac{0}{-16}
=0
$