Why did it take 38 years from the time luthers wrote hils ninety-five until luthersnism was accepted at the peace of augburg?

The Catholic Church and its major secular ally, the Holy Roman Emperor, were not about to give up their monopoly on power through Catholic Christianity without a fight.

This led to prolonged religious wars; by 1555 both sides were exhausted, and agreed the somewhat fudged Peace of Augsburg to paper over the cracks.