12n^2-8n-2=0

Solution for 12n^2-8n-2=0 equation:

12n^2-8n-2=0

a = 12; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·12·(-2)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{10}}{2*12}=\frac{8-4\sqrt{10}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{10}}{2*12}=\frac{8+4\sqrt{10}}{24}
$