y^2-1=12-6y^2

Solution for y^2-1=12-6y^2 equation:

y^2-1=12-6y^2

We move all terms to the left:

y^2-1-(12-6y^2)=0

We get rid of parentheses

y^2+6y^2-12-1=0

We add all the numbers together, and all the variables

7y^2-13=0

a = 7; b = 0; c = -13;
Δ = b2-4ac
Δ = 02-4·7·(-13)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{91}}{2*7}=\frac{0-2\sqrt{91}}{14}
=-\frac{2\sqrt{91}}{14}
=-\frac{\sqrt{91}}{7}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{91}}{2*7}=\frac{0+2\sqrt{91}}{14}
=\frac{2\sqrt{91}}{14}
=\frac{\sqrt{91}}{7}
$