Deduction of the formula of qudratic equation

Hello my friends of steemit, once again I'm bringing to You a post explaining one mathematic formula very known from the algebra, I'm talking about the quadratic equation and it's formula for the solution. In this publication I'm goin to show You the deduction of the solution of the qadratic equation, for this deduction we will use another formula of the algebra that we explain before: the notable product, Let get started.

We start writing the quadratic equation:

Now, we multiply all the equation by 4 , remember, in the right side of the equality we have the number zero, hence, 4.0 = 0. So we have:

Next step is to sum in both sides of the equality the quantity b^2:

Now we will move the quantity 4ac from the left side of the equality to the right side:

If we observe the left side of the last expression, there we have a notable product developed

Therefore, the left side of the equality we can write as follow:

Extracting the square root in both sides of the equality, and remembering that, the square root have two possible solutions, one positive and other negative, we'll have:

Finally we only have to tranpose the quantities b (this pass to the other side as negative) and 2a (pass to divide) in order to isolate the x, we arrive to:

Here we have our formula, the same that we have used many times, now we know how it is deduced.

References:

1. Algebra: Aurelio Baldor

2. https://ciencimat.wordpress.com/2010/03/16/una-historia-muy-curiosa/