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]
(..) Always held to the notion of fair exchange in all my dealings. You give me, I give you. A balance. No balance anymore. Could I have a drink? Dying is thirsty work. Wish it were wine. (..)2014 TvShow: Game of Thrones Title: Mockingbird Season: 4 Episode 7