The+Quadratic+Formula

I researched where the quadratic formula came from because we use it a lot in solving equations and I thought it might be interesting to know the history of it.

The Babylonians were the founders of the Quadratic Formula. They discovered it as early as 1800 B.C. and wrote the formula down on clay tablets. The mathematics of the Old Babylonian Period (1800 - 1600 B.C.) were more advanced than that of Egypt. Their "excellent sexagesimal [numeration system]. . . led to a highly developed algebra." They had a general procedure equivalent to solving quadratic equations, although they recognized only one root and that had to be positive. In effect, they had the quadratic formula. They also dealt with the equivalent of systems of two equations in two unknowns. They considered some problems involving more than two unknowns and a few equivalent to solving equations of higher degree.

Like the Egyptians, their algebra was essentially rhetorical. The procedures used to solve problems were taught through examples and no reasons or explanations were given. Also like the Egyptians they recognized only positive rational numbers, although they did find approximate solutions to problems which had no exact rational solution. In 628 C.E., Brahmagupta gave the first explicit solution of the quadratic equation:

" To the absolute number multiplied by four times the [coefficient of the] square, add the square of the [coefficient of the] middle term; the square root of the same, less the [coefficient of the] middle term, being divided by twice the [coefficient of the] square is the value.