Puzzle #191: Temperatures

Just a bit of chill outside, eh? As you may know, -40°C = -40°F. What is the value for x where x°C = -x°F or where x°F = -x°C?

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 1, 2017 at noon Pacific Time. I will post the answer shortly after.