Multiply through by -1: x2-2(k+2)x+9k=0,
Rewrite: x2-2(k+2)x=-9k,
x2-2(k+2)x+(k+2)2=-9k+(k+2)2,
(x-(k+2))2=-9k+k2+4k+4=k2-5k+4=(k-4)(k-1).
For two complex roots, (k-4)(k-1)<0. That means k-4<0 and k-1>0, that is, k<4 and k>1, so 1<k<4. (It's not possible for the alternative: k>4 but k<1, so we can reject this.)