Finding 3 unknowns wth units

You have a couple of errors in your sheet:

1. Never use "Given" twice in a row without "closing" the first
2. In order to make your first attempt work, you have to turn psi and delta.G into functions of the unknown epsilon.c Of course replacing those variables by the appropriate expressions, as you did in your second attempt, would work, too.
3. You forgot to define M.sd
4. You cannot write "find(....)=" in your case as this would force Mathcad to show a vector with elements of three different dimensions (length, area, dimensionless). Unfortunately this is not possible in Mathcad. Nevertheless you can assign the output of find() to a vector of three variables.