Solar Blyze already made his move.
He already left earlier that morning after his conversation with Marci and didn't waste any time.
Even though it was a pity that Solar wouldn't see Emma during lunchtime and see her expression if he poked at her about him knowing about Xion, this was important.
The reason for Solar attending classes was simply to fill his boredom by participating in the Mage Academy. This was also an opportunity of gathering information relevant to this particular day and age.
Now that Solar found an interesting piece of information though?
It was easy enough to skip classes in order to focus more on gathering news and actually figuring out where this Xion Draconi was.
This wasn't just finding enough dark secrets about Emma's husband.
… What kind of person would deny the fact that it was a good idea to have some information against the king of Akkadia?