I am finding different equations for the synthesis. My lecture handout suggests a reaction with Sodium tetrafluroborate and Sulfuric acid. This is fine but I have to remember this for an exam and that reaction looks extremely hard to remember/balance in an exam. A second way seems to be reaction of boron oxide with Calcium fluoride and Sulfuric acid. However, I cannot find consistent equations for this...
Wikipedia simply suggests that Boron oxide reacts with $\ce{HF}$ which is made in situ by the reaction between sulfuric acid and calcium fluoride:
$$\ce{B2O3 + 6HF -> 2BF3 + 3H2O}$$
It's easy to remember but I am reluctant to accept this because it excludes two of the reactants (sulfuric acid and calcium fluoride). Would it be acceptable to merge the formation of $\ce{HF}$ into the above equation - thus including all reactants:
$$\ce{B2O3 + 3CaF2 + 6H2SO4 -> 2BF3 + 3H2O + 3Ca(HSO4)2}$$
It's a little tricky to balance but not too hard to remember. Is there anything wrong with the above equation? I haven't seen it anywhere but only variations on it.