We use the modal adverb 总算 to describe some end result or long-awaited satisfaction. We usually use it in colloquial speech.
The adverb 总算 has strong emotional coloring. It emphasizes that an action that the speaker expected to happen eventually occurred after a long period of time.
At the end of sentences with the adverb 总算, we should state the particle 了 to indicate a change in the situation.
Mom finally came
māma zǒngsuàn lái le
The exams are finally over
kǎoshì zǒngsuàn jiéshù le
Sometimes we use the adverb 总算 in the meaning of “in general”. We usually use it when we give a general comment on a situation.