Babylonian mathematicians, as early as 2000 BC (displayed on

Old Babylonian clay tablets) could solve problems relating the areas and sides of rectangles. There is evidence dating this algorithm as far back as the

Third Dynasty of Ur.

Geometric methods were used to solve quadratic equations in Babylonia, Egypt, Greece, China, and India. The Egyptian

Berlin Papyrus, dating back to the

Middle Kingdom (2050 BC to 1650 BC), contains the solution to a two-term quadratic equation. Babylonian mathematicians from circa 400 BC and

Chinese mathematicians from circa 200 BC used

geometric methods of dissection to solve quadratic equations with positive roots.

These early geometric methods do not appear to have had a general formula.

Euclid, the

Greek mathematician, produced a more abstract geometrical method around 300 BC. With a purely geometric approach

Pythagoras and Euclid created a general procedure to find solutions of the quadratic equation. In his work

*Arithmetica*, the Greek mathematician

Diophantus solved the quadratic equation, but giving only one root, even when both roots were positive.

In 628 AD,

Brahmagupta, an

Indian mathematician, gave the first explicit (although still not completely general) solution of the quadratic equation

*ax*2 +

*bx* =

*c* as follows: "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." This is equivalent to:

en.wikipedia.org