Classify the graph of the equation

I have an equation that i think is an ellipse or hyperbola since looking at the equation it has a .

However, i am having problems finishing it since i think i have to do complete the square but cant seem to get it.

Heres the equation.

Wouldn't i arrange like terms

then, completing the square has me baffled.

First term i take half of

so i now have

would i then take half of 3 which is

If true then:

pull out the 4 on the left side - but not ure how to handle the second side?

simplifying the left side further

Any help is much appreciated..

Thank you

Re: Classify the graph of the equation