12n^2-20n-24=0

Solution for 12n^2-20n-24=0 equation:

12n^2-20n-24=0

a = 12; b = -20; c = -24;
Δ = b2-4ac
Δ = -202-4·12·(-24)
Δ = 1552
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:

$\sqrt{\Delta}=\sqrt{1552}=\sqrt{16*97}=\sqrt{16}*\sqrt{97}=4\sqrt{97}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{97}}{2*12}=\frac{20-4\sqrt{97}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{97}}{2*12}=\frac{20+4\sqrt{97}}{24}
$