He became desperate after his failure./His failure drove him to despair [desperation].
失恋してから彼はやけを起こした
He 「gave himself up [abandoned himself] to despair after his disappointment in love./After his disappointment in love, he ceased to care what happened to him.
やけになって花瓶をたたきつけた
He threw the flower vase to the floor in a fit of despair.