-4y^2-96y+172=0

Solution for -4y^2-96y+172=0 equation:

-4y^2-96y+172=0

a = -4; b = -96; c = +172;
Δ = b2-4ac
Δ = -962-4·(-4)·172
Δ = 11968
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:

$\sqrt{\Delta}=\sqrt{11968}=\sqrt{64*187}=\sqrt{64}*\sqrt{187}=8\sqrt{187}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-8\sqrt{187}}{2*-4}=\frac{96-8\sqrt{187}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+8\sqrt{187}}{2*-4}=\frac{96+8\sqrt{187}}{-8}
$