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With a formula, you know the variable's value, and you have to calculate the value of the function of it. With an equation, you know the function's value, and you have to calculate the value of the variable.
Formula is the one of the specific value. This is generates.
the value of
I could not figure out the math equation. The new data did not fit the existing equation. An equation can be a math formula or standard method.
You cannot plug in a variable, what you do is plug in the value for a variable. If you know the value of the variable in an equation (or formula), the process of replacing that variable whenever it appears in the equation by its value is called plugging in the value for the variable.