Classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola?

It is a hyperbola.

It is in the form of x^2-y^2=1

If you need help transforming the equation, I would be happy to help.

I would also recommend wolframalpha.com. It has came in handy for me plenty of times!

EDIT: I've been trying to transform this equation, and I'm getting some really odd numbers. I'll keep trying though!

EDIT #2: Alright, with a little help from WolframAlpha, I think I can explain this:

First group the terms together, and move to the other side of the equals sign:

(6x^2-9x)-(7y^2-6y)=-13

Now, factor out the 6 from the x-terms, and the 7 from the y-terms so that the x^2 and y^2 are by themselves.

6(x^2-3/2x)-7(y^2-6/7y)=-13

Now complete the square for both the x-terms and the y-terms

6(x^2-3/2x+9/16)-7(y^2-6/7y+9/49)=-13

6(x-3/4)^2-7(y-3/7)^2=-13+54/16-63/49

6(x-3/4)^2-7(y-3/7)^2=-611/56

Then divide both sides by -611/56 so that the equation equals -1.

336/611(x-3/4)^2-392/611(y-3/7)^2=-1