does this equation describe an ellipse? 5y^2-18x+7=20y+3x^2-16

this is what I did

-3(x^2+6x+9) + 5(y^2-4y+4)=-23+20+(-27)

-3(x+3)^2/-30 + 5(y-2)^2/-30=-30/-30

(x+3)^2/-10 + (y-2)^2/-6=1