y^2-13=6-5y^2

Solution for y^2-13=6-5y^2 equation:

y^2-13=6-5y^2

We move all terms to the left:

y^2-13-(6-5y^2)=0

We get rid of parentheses

y^2+5y^2-6-13=0

We add all the numbers together, and all the variables

6y^2-19=0

a = 6; b = 0; c = -19;
Δ = b2-4ac
Δ = 02-4·6·(-19)
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{-(0)-2\sqrt{114}}{2*6}=\frac{0-2\sqrt{114}}{12}
=-\frac{2\sqrt{114}}{12}
=-\frac{\sqrt{114}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{114}}{2*6}=\frac{0+2\sqrt{114}}{12}
=\frac{2\sqrt{114}}{12}
=\frac{\sqrt{114}}{6}
$