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Solve for x over the real numbers:
2+sqrt(x) = sqrt(x+12)

Raise both sides to the power of 2:
(2+sqrt(x))^2 = x+12

Subtract x+12 from both sides:
-12+(2+sqrt(x))^2-x = 0

-12+(2+sqrt(x))^2-x  =  4 sqrt(x)-8:
4 sqrt(x)-8 = 0

Add 8 to both sides:
4 sqrt(x) = 8

Divide both sides by 4:
sqrt(x) = 2

Raise both sides to the power of two:
Answer: |  x = 4

Square both sides of the equation to get:
4 + 4sqrtx +x =x+12        subtract 4   and  x   from both sides to get

4sqrtx =8                          Divide both sides by 4

sqrtx = 8/4 = 2                   Square both sides to get 'x'

x = 4