You have to build improvements to make them both happier and healthier. Happy needs a culture slider or some civic choices, healthy is a longer route unless you have some rice or corn etc. to hook up (paired with graneries for extra effect.)
Mostly you want to prevent this situation though. You can do in one of two ways:
1. Remove people from working tiles, and make them merchants, scientists, etc.
AND/OR
2. Take your people off of high food sources and redirect them to lower food/higher income or production locations.
Either way it slows or halts growth altogether. This is good since an unhealthy city will eventaully eat lots of food without giving much back, and an unhappy city doesn't do a whole lot for you. Focusing on specialists or production will help you immediately as well.
