y^2-13=16-10y^2

Solution for y^2-13=16-10y^2 equation:

y^2-13=16-10y^2

We move all terms to the left:

y^2-13-(16-10y^2)=0

We get rid of parentheses

y^2+10y^2-16-13=0

We add all the numbers together, and all the variables

11y^2-29=0

a = 11; b = 0; c = -29;
Δ = b2-4ac
Δ = 02-4·11·(-29)
Δ = 1276
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:

$\sqrt{\Delta}=\sqrt{1276}=\sqrt{4*319}=\sqrt{4}*\sqrt{319}=2\sqrt{319}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{319}}{2*11}=\frac{0-2\sqrt{319}}{22}
=-\frac{2\sqrt{319}}{22}
=-\frac{\sqrt{319}}{11}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{319}}{2*11}=\frac{0+2\sqrt{319}}{22}
=\frac{2\sqrt{319}}{22}
=\frac{\sqrt{319}}{11}
$