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]
(..) The Jedi are relentless. If they are not all destroyed, it will be civil war without end. First I want you to go to the Jedi temple. We will catch them off-balance. Do what must be done, Lord Vader. Do not hesitate. Show no mercy. Only then will you be strong enough with the dark side... (..)2005 Star Wars: Episode III - Revenge of the Sith
(..) I don’t think the boy can handle it. I don’t trust him. With all due respect, Master, is he not the chosen one? Is he not to destroy the Sith and bring balance to the Force? So the prophecy says. YODA: A prophecy that misread could have been. He will not let me down. He never has. (..)2005 Star Wars: Episode III - Revenge of the Sith