Nah, they are different.
Explicate will often be used when you are explaining something complex or philosophically deep.
It's true when you said that you would use explicate in academics, politics, finance, philosophic context and stuff. It indicates a very detailed explanation (including reasons why things are the way they are), and it is sometimes a complex one.
"He explicated the nature of political economy on foreign central governments."
Explain can be used for that same purpose or more common purposes, such as explaining instructions or very basic academic ideas. This may not include deep thinking and understanding of reasons behind ideas.
"He explained how to use the grill."
Also, I don't think explicate is a very formal form of explain though. You can use explain in formal writings too.