12n^2-24n-6=0

Solution for 12n^2-24n-6=0 equation:

12n^2-24n-6=0

a = 12; b = -24; c = -6;
Δ = b2-4ac
Δ = -242-4·12·(-6)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{6}}{2*12}=\frac{24-12\sqrt{6}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{6}}{2*12}=\frac{24+12\sqrt{6}}{24}
$