Solution of/to/for equation
Solution 1:
Prepositions are versatile words with overlapping meanings. There are several usages in English where more than one preposition could be used, with little or no change in meaning. Let me reiterate that: there are several usages in English where more than one preposition could be used, with little or no change of meaning.
The Ngram is interesting, but hardly surprising. There's no "official" correct preposition here.