Square both side to get
3x-h = (x+3)^2
distribute the squared
3x - h = x^2 + 6x + 9
subtract 3x from both sides
-h = x^2 + 3x + 9
The answer will only have real solutions if the right side is factorable
h= -19, and 2.25 are both values that would make the right side factorable