(8n^2)-12n-2=0

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

(8n^2)-12n-2=0

a = 8; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·8·(-2)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{13}}{2*8}=\frac{12-4\sqrt{13}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{13}}{2*8}=\frac{12+4\sqrt{13}}{16}
$