y^2-4y-76=0

Solution for y^2-4y-76=0 equation:

y^2-4y-76=0

a = 1; b = -4; c = -76;
Δ = b2-4ac
Δ = -42-4·1·(-76)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8\sqrt{5}}{2*1}=\frac{4-8\sqrt{5}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8\sqrt{5}}{2*1}=\frac{4+8\sqrt{5}}{2}
$