Y=-8x^2-96x+5

Solution for Y=-8x^2-96x+5 equation:

=-8Y^2-96Y+5

We move all terms to the left:

-(-8Y^2-96Y+5)=0

We get rid of parentheses

8Y^2+96Y-5=0

a = 8; b = 96; c = -5;
Δ = b2-4ac
Δ = 962-4·8·(-5)
Δ = 9376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9376}=\sqrt{16*586}=\sqrt{16}*\sqrt{586}=4\sqrt{586}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-4\sqrt{586}}{2*8}=\frac{-96-4\sqrt{586}}{16}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+4\sqrt{586}}{2*8}=\frac{-96+4\sqrt{586}}{16}
$