6y^2-2y-4=12

Solution for 6y^2-2y-4=12 equation:

6y^2-2y-4=12

We move all terms to the left:

6y^2-2y-4-(12)=0

We add all the numbers together, and all the variables

6y^2-2y-16=0

a = 6; b = -2; c = -16;
Δ = b2-4ac
Δ = -22-4·6·(-16)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{97}}{2*6}=\frac{2-2\sqrt{97}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{97}}{2*6}=\frac{2+2\sqrt{97}}{12}
$