Y=8x^2+8x-96

Solution for Y=8x^2+8x-96 equation:

=8Y^2+8Y-96

We move all terms to the left:

-(8Y^2+8Y-96)=0

We get rid of parentheses

-8Y^2-8Y+96=0

a = -8; b = -8; c = +96;
Δ = b2-4ac
Δ = -82-4·(-8)·96
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-56}{2*-8}=\frac{-48}{-16}
=+3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+56}{2*-8}=\frac{64}{-16}
=-4
$