complicated cas problem

[Arno K]

You will have to take into account that the calc will not try to simplify first, so it has to deal with a transcendental equation, I think you should try fsolve() here, that gives you the required [4.].    
Arno
Edit: This even works when I define y:="left-side" and z:="right-side", without the intervall there is a message telling you to better use an interval for bisection.