We need to solve these equations equating radii
x^2 + y^2 = ( x + 3)^2 + (y -2)^2
x^2 + y^2 = x^2 + 6x + 9 + y^2 - 4y + 4
4y - 6x = 13 (1)
And
x^2 + y^2 = (x + 2)^2 + (y -1)^2
x^2 + y^2 = x^2 + 4x + 4 + y^2 -2y + 1
2y - 4x = 5 multiply this through by -2 → -4y + 8x = -10 ( 2)
Add (1) , (2)
2x = 3
x = 3/2
And
2y - 4(3/2) = 5
2y - 6 = 5
2y = 11
y = 11/2
Center = ( 3/2 , 11/2)