How to split profit after breakup

[Christina Babayan]

My ex and I bought a house together in 2014. I put down $34,933, and he put down $0. I know we should have made an agreement at the time, so I'm definitely paying for it now. We split the mortgage in half until September of 2015 when he and his girls moved out. I stayed, and have continued to pay the mortgage alone. Including the month of May, I have put in $37,433 total mortgage. He has put in $15,098. He also owes me $8,738 which has been agreed on and I want it included in doing this math.  I placed the house on the market 8 days ago for $407,900. We have $291,000 left on mortgage. How do we split this. He claims he should get $20,000. Only mistake was to put his name on the papers. Thank you for your help!