​ What is the solution of the equation?

 √ [ 2x - 3 ]  + 3  =  x        subtract 3 from both sides

 √ [ 2x - 3 ]  =  x - 3        square both sides

2x - 3   =  x^2 - 6x + 9       subtract/add   2x, 3  to both sides

0  = x^2 - 8x + 12      factor

(x - 6) ( x - 2)  = 0

Setting each factor to 0  and solving for x  gives x  = 6  and x  =  2

Only the first solution solves the original problem