Expressing “to worry” with 担心 and 操心
These verbs are similar in meaning, but they are used in different contexts.
The verb 操心
We use the verb 操心 
to emphasize that a person is uneasy and thinking a lot about a problem. He may be spending a lot of energy finding a solution.
to emphasize that a person is uneasy and thinking a lot about a problem. He may be spending a lot of energy finding a solution.Examples
他运气真好，从来不用为金钱操心
He is so lucky that he never has to worry about money
tā yùnqì zhēn hǎo, cónglái bú yòng wèi jīnqián cāoxīn
为孩子操心是很自然的
It's natural to worry about your children
wèi háizi cāoxīn shì hěn zìrán de
我此刻不想让她为我的事操心
I don't want her to worry about me right now
wǒ cǐkè bù xiǎng ràng tā wèi wǒ de shì cāoxīn
We usually do not state any object after 操心.
For example, to say “I'm worrying about you”, we should say 我为你操心 .
We cannot say 我操心你.
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We cannot say 我操心你.The verb 担心
We use the verb 担心 to emphasize that one is worried about someone or something. However this verb does not imply that the person is doing something toward finding a solution.
to emphasize that one is worried about someone or something. However this verb does not imply that the person is doing something toward finding a solution. Pay attention
We can state the object after the verb 担心.
Examples
我担心这种疗法是否安全
I am worrying about the safety of this therapy
wǒ dānxīn zhè zhǒng liáofǎ shìfǒu ānquán
我有点担心他
I'm a little worried about him
wǒ yǒudiǎn dānxīn tā
我们担心他的精神状况
Мы обеспокоены его психическим состоянием
wǒmen dānxīn tā de jīngshén zhuàngkuàng