What must I do to compensate for 120 days of prayer missed due to delaying them for studying?

Prayer is a great pillar and the first thing a servant will be held accountable for. If you delay a prayer beyond its time and then pray it, you have sinned, but your obligation is fulfilled. However, if you do not pray it at all, you must make up for what you missed. The way to make up for missed prayers is to pray what you can each day in addition to the five current prayers, in a manner that does not harm your body or your livelihood. You continue this until you have made up all missed prayers. It is more cautious to make up the prayers in their proper order, even though disrupting the order does not invalidate the prayer.