6y^2=12y+13=2y^2+4

Solution for 6y^2=12y+13=2y^2+4 equation:

6y^2=12y+13=2y^2+4

We move all terms to the left:

6y^2-(12y+13)=0

We get rid of parentheses

6y^2-12y-13=0

a = 6; b = -12; c = -13;
Δ = b2-4ac
Δ = -122-4·6·(-13)
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{114}}{2*6}=\frac{12-2\sqrt{114}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{114}}{2*6}=\frac{12+2\sqrt{114}}{12}
$