c. After doing some complicated calculations and working out, I finally found the answer, which is 137.68638.
d. After doing some complicated calculations and working out, I finally found the answer to be 137.68638.
e. After doing some complicated calculations and working out, I finally found the answer - 137.68638.
These three are correct, with perhaps slightly different subtext meanings:
(c) suggests "I found the answer. The answer is 137.68638". It is a statement of one primary fact, and by the way, of a secondary fact.
(d) suggests "I found that the answer is 137.68638" - it is a statement of one fact.
(e) suggests something of "I found the answer! (wait for it...) 137.68638!", it creates some suspense between announcing the finding of the answer and telling us what it is.
The other two sentences sound wrong to me.
Your other example is of a different structure and "of" seems correct there, but it would not be correct here.
Edit: the sentence with "the answer of" (which was not one of the original options) may be gramatically correct, but it is unusual to refer to the answer this way. This was asked before but the answer there wasn't detailed enough. The way "of" is typically used is to denote the entity providing the answer, rather than the answer itself, such as in Proverbs 16:1
The preparations of the heart in man, and the answer of the tongue, is from the LORD.
Obviously, here, "the tongue" is not the answer.