4n^2-96n-24=0

Solution for 4n^2-96n-24=0 equation:

4n^2-96n-24=0

a = 4; b = -96; c = -24;
Δ = b2-4ac
Δ = -962-4·4·(-24)
Δ = 9600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-40\sqrt{6}}{2*4}=\frac{96-40\sqrt{6}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+40\sqrt{6}}{2*4}=\frac{96+40\sqrt{6}}{8}
$