"He wishes to eat."
Translation:Él desea comer.
The "a" is often added when the first verb involves movement or the verb "ir" (vamos a comer = we are going to eat) but not with a verb like desear
I believe it is because... When you say 'Él desea a comer', it means 'He wishes to to eat'. Why? The to is included in comer because it is the infinitive form translating to 'to eat'. The a is unnecessary when it comes to a 'verb+infinitive' phrase. There is an exception to this, which rspreng is talking about. It is the 'ir + a + infinitive' phrasing, which is used as a way to express future events.
I think you only need the "a" in there if desear is followed by a noun. E.g. "El desea a ella" (he desires her). But if it's a verb that follows, then you omit the preposition (a).
I'm not so sure about that. I think that "Él la desea" would be the proper way to say it, rather than "Él desea a ella".