Proto-Indo-European *seǵʰ- "to hold". The zero-grade form *sǵʰ- became Ancient Greek σχολή skholē which meant "stop, leisure", moving to "study," then "a place for study, school". This was borrowed into Latin as schola, then borrowed into Old English as scōl, which became English school, the h being added to the word to reflect the word's Latin/Greek origin.
The suffixed form *seǵʰ-es- became Ancient Greek ἔχω ekhō "to hold, possess, have", and ἑκτικός hektikos "habitual, customary, enduring", borrowed into Latin as hecticus, becoming Old French etique, then borrowed into Middle English as etik "recurring, consumptive". This became hectic in the 1500s, the h and c being added again to reflect the word's Latin/Greek origin. The word's meaning moved from "consumptive" to "feverishly intense activity" c1900.