He's trying to keep his work life and his family life 'in balance'. = He's trying to keep his work life 'in balance with' his family life. [=he's trying to give a proper of amount of time and attention to both his work life and his family life]
The discount 'balances out' the shipping charge. = The discount and the shipping charge 'balance' each other 'out'. [=the shipping charge and the discount together equal zero]
He needs to achieve/create/strike a better 'balance' between his work life and his family life. [=he needs to spend less time at work and more time with his family]
(..) - Hello. You saved my life. - l haven't forgotten. l thought you were very, very tall. You seemed so big and... giant. l felt like a child who can't keep her balance. - A toddler. - A toddler. My hair wss long at some point. l've forgotten what a nuisance it is to wssh. (..)1996 The English Patient