Need help figuring out how to write and equation in the standard form of an ellipse.

So I have the equation:

$\displaystyle 3x^2+4y^2+8y=8$

I'm pretty sure its an ellipse so I tried to start putting it in the standard form of an ellipse.

$\displaystyle 3x^2+4y^2+8y=8$

$\displaystyle 3x^2+4(y^2+2y+1)=8-4$

$\displaystyle 3x^2+4(y+1)^2=4$

$\displaystyle 3x^2/4+(y+1)^2=1$

$\displaystyle x^2/4+(y+1)^2/3=1/3$

But how can I make the right side equal 1 instead of 1/3 and not having thing multiplying by x or y?