Getting Particular number from optimization

Hello,

I am trying to find a particular number from a basic math formula using optimization method so it can tweak slider on it own. For example: if x/y + y/z + z/x = 6.125 , my input would be with three sliders for each x,y,z and I need combinations of different numbers giving 10

if x = 16, y = 4, z = 2 it gives 6.125 from above equation but I need all possible combinations within certain range. Is it possible to set galapogos or octopus to find particular combination for the number we need?