Equations are statements that use numbers and symbols to demonstrate that two groups of mathematical data are equal. The roots or solutions to an equation are numbers that replace the variables (unknown quantities) to make the equation true.

The first records of equations come from early Greek scholars, 540 B.C.-250 B.C. Euclid, Pythagoras, and his Pythagorean followers used algebraic problems with geometric proofs. This method of mixing algebra and geometry led to complex constructions. The Greek system of mathematics used layers of numbers, letters, and punctuation marks piled on top of each other. This approach probably favored interpretations of geometry rather than arithmetic calculations. Other early mathematical records show that Egyptians, Indians, Muslims, and Greeks have been using cubic equations for more than 2000 years.

Some of the best known categories of equations include:

• Algebraic equations: The variables appear with coefficients that can have addition, subtraction, multiplication...