Hi guys, need help with this question:

Find the 2 complex numbers z1 and z2 each of which satisfies the following EQN:

3zz* + 2(z-z*) = 39 + 12i

To solve this, I let z = x + yi

3zz* + 2(z-z*) = 39 + 12i

=> 3(x^2 + y^2) + 2y = 39 + 12i

Equating Real and Imaginary parts:

3x^2 = 39 => x = sq root 13

3y^2 + 2y = 12 => y = (-1/3) + sq root (37/9)

However, my ans was wrong. Any idea what went wrong? Thanks in advance!