Y=4x2-4x-24

Solution for Y=4x2-4x-24 equation:

=4Y^2-4Y-24

We move all terms to the left:

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

We get rid of parentheses

-4Y^2+4Y+24=0

a = -4; b = 4; c = +24;
Δ = b2-4ac
Δ = 42-4·(-4)·24
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-20}{2*-4}=\frac{-24}{-8}
=+3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+20}{2*-4}=\frac{16}{-8}
=-2
$