6y^2-2y-7=2

Solution for 6y^2-2y-7=2 equation:

6y^2-2y-7=2

We move all terms to the left:

6y^2-2y-7-(2)=0

We add all the numbers together, and all the variables

6y^2-2y-9=0

a = 6; b = -2; c = -9;
Δ = b2-4ac
Δ = -22-4·6·(-9)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{55}}{2*6}=\frac{2-2\sqrt{55}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{55}}{2*6}=\frac{2+2\sqrt{55}}{12}
$