Puzzle #192: More Temperatures

It is warming up, and one of the answers to this one is rather warmer. What is the value for x where 2x°F = x°C or where 2x°C = x°F?

There are two answers.

Submit your answer to Gene Wirchenko <genew@telus.net>. Your answer should be in the form of a proof. That means to show how your answer must be correct. The deadline is Wednesday, February 8, 2017 at noon Pacific Time. I will post the answer shortly after.