y^2-3=14-10y^2

Solution for y^2-3=14-10y^2 equation:

y^2-3=14-10y^2

We move all terms to the left:

y^2-3-(14-10y^2)=0

We get rid of parentheses

y^2+10y^2-14-3=0

We add all the numbers together, and all the variables

11y^2-17=0

a = 11; b = 0; c = -17;
Δ = b2-4ac
Δ = 02-4·11·(-17)
Δ = 748
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:

$\sqrt{\Delta}=\sqrt{748}=\sqrt{4*187}=\sqrt{4}*\sqrt{187}=2\sqrt{187}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{187}}{2*11}=\frac{0-2\sqrt{187}}{22}
=-\frac{2\sqrt{187}}{22}
=-\frac{\sqrt{187}}{11}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{187}}{2*11}=\frac{0+2\sqrt{187}}{22}
=\frac{2\sqrt{187}}{22}
=\frac{\sqrt{187}}{11}
$