A friend of mine asked for some help with a design of speaker-stands, 3 thick bits of wood formed into a Z shape, but what angle to cut? That fairly quickly reduced to solving a quadratic, but how to solve that? This was pre-internet, I'd done the derivation at school but that was a while ago, so I spend 2 days working the sod out. I enjoyed it so much that I went to the local University and asked if I could get on the maths degree program, they said yes. That changed my life.
He never made those speaker-stands.