y^2-20Y-96=0

Solution for y^2-20Y-96=0 equation:

y^2-20-96=0

We add all the numbers together, and all the variables

y^2-116=0

a = 1; b = 0; c = -116;
Δ = b2-4ac
Δ = 02-4·1·(-116)
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{29}}{2*1}=\frac{0-4\sqrt{29}}{2}
=-\frac{4\sqrt{29}}{2}
=-2\sqrt{29}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{29}}{2*1}=\frac{0+4\sqrt{29}}{2}
=\frac{4\sqrt{29}}{2}
=2\sqrt{29}
$