Question

What is the solution of sqrt x+12=x

Answer 1

X=4 
here is the work: https://www.tiger-algebra.com/drill/sqrt(x_12)=x/

Answer 2

Sqrtx = x - 12
x = (x -12)^2
x^2 - 24x - x + 144 = 0
x^2 -25x + 144 = 0
(x - 16)(x - 9) = 0

x = 9, 16 

Check  to see if these fit the equation:-

x = 16 :-
sqrt16 + 12 = 16
16 = 16  So  x =16 is a root

x = 9:-

sqrt9 + 12 = 9
3 + 12 = 9  This is NOT a root 

There is only one root which is  x = 16.  9 is  an extraneous root which you get sometimes in equations containing radicals.