Throughout the years, the history of mathematics has taken its fair share of changes. It has stretched across the world from the Far East, migrating into the Western Hemisphere. One of the most fundamental and key principles of mathematics has been the quadratic formula. Having been used in several different cultures, the formula has been part of the base of mathematics theory. The general equation has been derived from many different sources, most commonly: ax2 + bx + c = 0, with x being the variable and a, b, and c its respective constant terms. Though this is how modern mathematics perceives the equation, different symbols and notations have been used to represent the formula.

Beginning in the "Before Christ- era, the Babylonians were the first to have been recorded demonstrating the equation, circa 400 BC. The form most mathematics students use today is: .

To solve a quadratic equation the Babylonians essentially used the standard formula, with the a term being included in the x2 variable. They considered two types of quadratic equations, namely: .

x2 + bx = c and x2 - bx = c.

Here b and c were positive but not necessarily integers. The form that their solutions took was, respectively: .

x = [(b/2)2 + c] - (b/2) and x = [(b/2)2 + c] + (b/2).

Notice that in each case this is the positive root from the two roots of the quadratic and the one that will make sense in solving "real" problems. For example problems which led the Babylonians to equations of this type often concerned the area of a rectangle. For example if the area is given and the amount by which the length exceeds the width is given, then the width satisfies a quadratic equation and then they would apply the first version of the formula above (website one). .

The efforts the Babylonians made at using this method were far from futile and, actually, served a very important purpose. .

It was an important task for the rulers of Mesopotamia to dig canals and to maintain them, because canals were not only necessary for irrigation but also useful for the transport of goods and armies.