How it should play out for punishment is Solo getting arrested and living out the rest of his days behind bars. 'Cause y'know. Murder.
Technically the fight on the first day was equal blame to both parties, though, Solo just won. Not so much this time, but others came to help.
No one died, though; Solo was more likely to die in that battle anyways.
The headmaster is probably laughing his ass off right now.