Find the product of all real values of \(r\) for which \(\frac{1}{2x}=\frac{r-x}{7} \) has exactly one real solution.
Let's make these have an equal denominator first...
\(7/14x = 2x(r-x)/14x\)
That will get us \(0=2x(r-x)/14x - 7/14x=0\)
Can you get it from here, or do you need more help?