The Quadratic formula was used for several thousand years. The quadratic equation had also changed on occasions.
The quadratic formula is:
x1,2=(-b/2a) ± (1/2a)(b2-4ac)1/2
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Around 2000 years back, the Chinese, Egyptians and Babylonians were already familiar with the area of a square level with length of its every side. By using hay bales, they figured out that they could stack together more nine bales if the length of roof space were wide almost three times. The area of the other complex shapes could also be computed.
However, they knew how the sides of the shapes could be worked out and they had faced a little big problem. They should have known how the lengths of the sides are calculated. The shape had to be leveled with total area with the length of sides.
The use of Quadratic formula by Egyptians
About 1500 years back, Egyptians had not used numbers like they are used today. Words were used for expressing mathematical problems. However the scripture avoided the issue of quadratic equation by solving the areas of every side and constructed a chart. They made something similar to a multiplication table. Computation was made quick and fast. The Egyptians did require computing all sides and shapes every time. They only had to refer to the chart.
These tables still exist today. They might be mathematically incorrect but they surely show the beginning of the quadratic formula.
The use of Quadratic formula by Babylonians
The Babylonians had adopted a diverse way for solving problems. They used numbers instead of words, in contrast with the Egyptians. The numbers used by the Babylonians were a lot more the same like the numbers used today although they were based on a hexadecimal model. Addition and multiplication were easier to do with this system. Around 1000 BC, Babylonian engineers could check the authenticity of their values. By 400 BC, they discovered a technique called 'completing the square' for solving problems with areas.
Euclid and Pythagoras
The first mathematical attempt to invent a quadratic formula was performed in 500 BC by the Pythagoras. Euclid did same in Egypt. He used a simple geometric method and came up with a formula for solving the equation. The Pythagoras had observed that ratios did not add up between area of square and length of sides and there was no other ratio except rational. Euclid had uniquely thought that there would be irrational numbers just like there are rational numbers. He later released a book called 'Elements' and explained the mathematics for solving quadratic equations in it. However his equation was not using the same formula which is known today, his formula could not calculate a square root.
How 0 was added to the equation by Hindu mathematicians
Hindu mathematicians created the concept of 0 which meant nothing. The Western mathematics had believed this value of nothing. Brahmagupta was a Hindu mathematician who used irrational numbers by 700 AD. He discovered two roots in the answer but roughly around the 1100 AD, another Hindu mathematician came up with a discovery that any positive number had two square roots.
How Quadratic Equation was introduced in Europe
A well known Muslim mathematician named Mohammad Al-Khwarismi successfully solved the quadratic equation in around 820 AD. He had not used numbers or negative solutions. As his word spread, a Jewish mathematician named Abraham Hiyya brought this knowledge to Spain in 1100. Since then, mathematicians from Europe picked and started using the equation.
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