n^2-96n-24=0

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

n^2-96n-24=0

a = 1; b = -96; c = -24;
Δ = b2-4ac
Δ = -962-4·1·(-24)
Δ = 9312
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:

$\sqrt{\Delta}=\sqrt{9312}=\sqrt{16*582}=\sqrt{16}*\sqrt{582}=4\sqrt{582}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-4\sqrt{582}}{2*1}=\frac{96-4\sqrt{582}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+4\sqrt{582}}{2*1}=\frac{96+4\sqrt{582}}{2}
$