Question 327788
{{{x^2+y^2-5x+3y=0}}}

Group the x and y terms:

{{{x^2-5x+y^2+3y=0}}}

Now, complete the square for each by adding the square of half the coefficient of x to both sides, then factor. 

{{{x^2-5x+25/4=(x-5/2)^2}}}

{{{y^2+3y+9/4=(x+3/2)^2}}}

Remember, the 25/4 and 9/4 have to be added to the right side as well.

{{{25/4+9/4=17/2}}} on the right side.

So, we have 

{{{(x-5/2)^2+(x+3/2)^2=17/2}}}

The center is at (5/2,-3/2) and the radius is {{{sqrt(17/2)}}}