The equation is:

3x^2-20y^2=80y+48

I know it is a hyperbola once I check with Wolfram Alpha. But, I need a definite way of knowing it is.

I tried setting it up in the standard form by trying to isolate 48.

3x^2-20y^2-80y=48

Then divide by 48 to make the right side equal 1 like the standard form for it is.

3x^2/48-(20y^2-80y)/48=1

But that is still not its standard form because I don't know what y^2 is... how can I get it to be just y^2?