Noun + する, をする is a very common construction in Japanese. Most of the nouns were originally imported from Chinese, and while nouns and verbs have the same forms in Chinese, する, をする (to do) are added to nouns to turn them into verbs in Japanese.
- 安心する、安心をする (feel relieved)
- 勉強する、勉強をする (study)
- 計画する、計画をする (plan)
- 発見する、発見をする (discover)
Obviously when the noun is modified by an adjective (clause), をする will be used.
- 彼は新しい元素を発見した -> He discovered a new element
- 彼は人類の起源について新しい発見をした -> He made a new discovery on the origin of humans
- 彼は経済を勉強している -> He studies economy
- 彼は経済の勉強をしている -> He studies economy
However either will be used in cases like below. Often it is just a matter of the speech rhythm. There is no practical difference between the two forms in terms of formality, literariness and so on, and they are fully interchangeable.
- 良い知らせを聞いて安心 (を) した -> I’m relieved to hear the good news
- 一つ質問 (を) してもいいですか？-> Can I ask a question?
- 心配 (を) する必要は無いですよ -> There is no need to worry