Can't manage your stubborn little brother who won't do what anyone says? You could call him intractable, or you could call your mother. Problems are intractable when they can't be solved.
Intractable means not tractable. Helpful, right? No? Let's break it down. In both words you see the word tract. A contract is a written document that explains how a legal situation is to be managed together. When someone is tractable they are able to be managed or handled. When they are intractable, they are as unmanageable as a hungry two-year old.