2y^2+6-y^2=9

Solution for 2y^2+6-y^2=9 equation:

2y^2+6-y^2=9

We move all terms to the left:

2y^2+6-y^2-(9)=0

We add all the numbers together, and all the variables

y^2-3=0

a = 1; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·1·(-3)
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3}}{2*1}=\frac{0-2\sqrt{3}}{2}
=-\frac{2\sqrt{3}}{2}
=-\sqrt{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3}}{2*1}=\frac{0+2\sqrt{3}}{2}
=\frac{2\sqrt{3}}{2}
=\sqrt{3}
$