The Hindu solution to the quadratic equation is the most elegant and simplest in comparison to the current method used. It avoids the need to use fractions, which makes the derivation very easy to perform. Almost all Hindu temples from the earliest period in history used this as the basis of its construction.
First, we move the c coefficient to the other side.
Then, multiply throughout by 4a. The ancient manuscripts express it as four times the first coefficient.
As you can see, we now have an a²x² term on the LHS, which is useful for making the square.
Then add b² to both sides.
As you can see, we can now complete the square.
Now take a square root on both sides, and as you can see we have a discriminant that is clean of any fractions.
We can now bring the b coefficient to the other side.
Then divide both sides by 2a, to give the famous formula. It is without a doubt that this is a much better method than what schools currently teach.