you are right so far, now complete the square

x^2 + y^2 = 3y

=> x^2 + y^2 - 3y = 0

=> x^2 + y^2 - 3y + (-3/2)^2 - (-3/2)^2 = 0

=> x^2 + y^2 - 3y + (-3/2)^2 = (-3/2)^2

=> x^2 + (y - 3/2)^2 = 9/4

=> x^2 + (y - 3/2)^2 = (3/2)^2

this is a circle with center (0, 3/2) and radius 3/2