Formula vs Equation

An expression with equals sign. The main purpose for equations in mathematics is to describe problems in real life in a way that mathematicians can deal with. 

Example: The equation \(y=x^{2} + ln\left ( x\right ) - 7\).

According to, a formula is a set of instructions for creating a desired result. Therefore, generally speaking: A formula is usually a general rule that takes the form of equation, and this sort of equation is usually proofed to be true in order to be used and solve other equation.

Example: The Euler Formula: \(e^{i\theta} = cos \left ( \theta \right ) + isin\left ( \theta \right )\) which was introduced by Leonhard Euler have been used in massive complex cases. 

Nevertheless, you might encounter some false exchange between these two terms while reading some test books. 

For instance:  Many people uses the term "quadratic equation" to describe the "quadratic formula" instead. In fact the quadratic formula is used to solve the quadratic equation of the form \(Ax^{2} + Bx+C =0\).