6a^2-8a-2=0

Solution for 6a^2-8a-2=0 equation:

6a^2-8a-2=0

a = 6; b = -8; c = -2;
Δ = b2-4ac
Δ = -82-4·6·(-2)
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*6}=\frac{8-4\sqrt{7}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*6}=\frac{8+4\sqrt{7}}{12}
$