Yeah, the solution set is {1/16, 0}
Jamesman explained how to get 1/16.
You get 0 by taking the original equation:
x - 4xsqrt(x) = 0
and factoring out x:
x[1-4sqrt(x)] = 0
This leaves you with two choices, either x = 0 or 1-4sqrt(x) = 0.
These choices lead to the two answers.