Y=4x^2-24x

Solution for Y=4x^2-24x equation:

=4Y^2-24Y

We move all terms to the left:

-(4Y^2-24Y)=0

We get rid of parentheses

-4Y^2+24Y=0

a = -4; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-4)·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*-4}=\frac{-48}{-8}
=+6
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-4}=\frac{0}{-8}
=0
$