6y^2-6y-2=0

Solution for 6y^2-6y-2=0 equation:

6y^2-6y-2=0

a = 6; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·6·(-2)
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{21}}{2*6}=\frac{6-2\sqrt{21}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{21}}{2*6}=\frac{6+2\sqrt{21}}{12}
$