Question 1030904
You want to adjust the equation into whichever standard form will fit variables and coefficients.  You will probably need to Complete the Squares to do this.


{{{3(x^2+(2/3)x)+15(y^2-(4/15)y)=30}}}


{{{3(x^2+(2/3)x+(1/3)^2)+15(y^2-(4/15)y+(2/15)^2)=30+3(1/3)^2+15(2/15)^2}}}, for which you need to understand the lesson on Completing the Square;


{{{3(x+1/3)^2+15(y-2/15)^2=30+10/3+4/15}}}


{{{3(x+1/3)^2+15(y-2/15)^2=30+50/15+4/15}}}


{{{3(x+1/3)^2+15(y-2/15)^2=30+54/15}}}


{{{3(x+1/3)^2+15(y-2/15)^2=30+18/5}}}


{{{(x+1/3)^2+5(y-2/15)^2=10+6/5}}}---------------Although finishing the equation into standard form is still not finished, you see that the expression with x and the expression with y have POSITIVE coefficient, and the constant righthand members is also positive; but the coefficients on the left member's expressions are unequal.  The equation will be for an ELLIPSE.