How do you create equations and use them to solve problems?

With models.

Step-by-step explanation:

Equations are models translated into math. When a phenomenon is being study, the variables in the experiment are being test between them to establish the relation beneath.

During the experiment is found if their relation is directly or inverse proportional. After that process of founding the possible relation, a constant needs to be calculated (experimentally) that will balance the equation. The constant is crucial to establish that equality on equations.

More or less, this is the way that equations are created to problems. That's why take a lot of time to create a model for some theory, of physics lest say.

Imagine the great Albert Einstein needed help from mathematicians to create equations for his theory, that's how difficult is this.