For what values of h does the equation have real solutions.

√ (3x-h) = x+3

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