Can't you just plug in the value 3 for x?
What do you mean by formal definition of a limit?
∀ϵ>0 show ∃δ∋|x−3|<δ⇒|3x+4−13|<ϵ
|3x+4−13|<ϵ⇒|3x−9|<ϵ⇒−ϵ<3x−9<ϵ⇒9−ϵ<3x<9+ϵ⇒3−ϵ3<x<3+ϵ3|x−3|<ϵ3
so choose δ=ϵ3and working everything backwards you end up with|3x+4−13|<ϵas desired