Maple; Find real solutions

$$y = k^{2}-4kx+3 - \sqrt{k^2+x-1/2}=0$$

I need to find the range of k so that this equation has some real solutions, using Maple.

I have started off by typing 'soln1:=solve(y,x);' which gives me two solutions both involving k. I just need to know how to get maple to return the range of k so that soln1 is real.

I can do it by hand, because I would just find out where the roots were undefined, right ? and exclude that from the range. But no idea how to do this in maple!!

Can anybody help?? Thanks