The simplest answer I can give you here is to say that in many contexts they are roughly synonymous - in other words similar in meaning and therefore sometimes used interchangeably, where the basic meaning is to find a solution or answer to a problem.

For example, we could say either "we have solved the problems in management" or "we have resolved the problems in management". To resolve a problem, argument or difficulty means to deal with it successfully. As in the example, "The cabinet met to resolve the dispute."

However, be aware that 'resolve' can be used with the infinitive with a slightly different meaning. If you resolve to do something you make a firm decision to do it.

"They resolved to take action."

'Resolve' also sometimes appears as a noun meaning a determination to do something. "We must be firm in our resolve to oppose them."

So Lilia, you'll find more examples in your dictionary, but in them meantime, I hope I've clarified the key differences there.

See also:
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