To any/every person, having introductory mathematical level, should be clear, that this equation 
has infinitely many solutions in real numbers (the cardinality of the set of solution is CONTINUUM).


Therefore, in order for the problem would make sense, it is reasonable to restrict the solution set by positive integer numbers.


Then one solution is easy to guess: it is  x= 5, y= 4, z= 5.


It is not difficult to guess the second solution: x= 6, y= 4, z = 16.


Actually, this equation has infinitely many solutions even in integer numbers.


Indeed, take x arbitrary positive integer greater than or equal to 5;

        take y= 4;

        then adjust z using the formula  z =  - 20.