"Find alpha, beta, and gamma:"

I'm thinking this looks like a predictor-corrector equation. But I'm a bit confused as to how to start. Is this gonna be a situation of expanding all the f's via Taylor's and just plugging in on the right side? If there's more to it, what would that be?

Also, we've got three unknowns in one equation. Does that mean there will be two "free" variables, not just one?