Y=12x2-18x

Solution for Y=12x2-18x equation:

=12Y^2-18Y

We move all terms to the left:

-(12Y^2-18Y)=0

We get rid of parentheses

-12Y^2+18Y=0

a = -12; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-12)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-12}=\frac{-36}{-24}
=1+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-12}=\frac{0}{-24}
=0
$