Question 441189
Let x the first unknown number, since their product is 30 the other unknown

number is {{{30/x}}}, and their average is:{{{(x+30/x)/2=(x^2+30)/2x)}}}.

This average {{{(x^2+30)/2x=6}}}, solving this quadratic equation we get:

{{{x^2-12x+30=0}}} => {{{x=(12+-sqrt(12^2-120))/2}}}, two values for the first 

number x:{{{x=6+sqrt(6)}}} and {{{{x=6-sqrt(6)}}}.

We have also two values for the second number:{{{30/(6+sqrt(6))}}}, and, 

{{{30/(6-sqrt(6))}}}. As you see the problem has two solutions.