Maxima gives us the following solutions: MaxSol1and2.gif.
I think that the simplest variants of solutions are those for K=2 and c=sqrt(3)=3^(1/2) (I assume that K>0 and c>0): MaxSol3.gif and MaxSol4.gif.
P.S. Use Maxima http://maxima.sourceforge.net/download.shtml
- it's free, open source and effective for the problems like this one.