---
title: "Quadratic Equation: a*x^2+b*x+c = 0"
description: "We all know about quadratic equation. We had solved it many many times in school. Let's recall about..."
author: "Madiyar92"
published: "2015-12-29T17:52:30+00:00"
modified: "2015-12-29T17:56:49+00:00"
locale: "ru"
canonical_url: "https://yvision.kz/post/quadratic-equation-a-x-2-b-x-c-0-623232"
markdown_url: "https://yvision.kz/post/quadratic-equation-a-x-2-b-x-c-0-623232/markdown"
site_name: "Yvision.kz"
---

# Quadratic Equation: a*x^2+b*x+c = 0

> We all know about quadratic equation. We had solved it many many times in school. Let's recall about...

We all know about quadratic equation. We had solved it many many times in school. Let's recall about quadratic equation.

Quadratic Equation is a second-order polynomial equation in a single variable:

![Quadratic Equation: a*x^2+b*x+c = 0](http://storage.yvision.kz/images/user/madiyar92/0ixER4O0GGOMP94kEwJXm6o2C49y4L.png)

Solutions for **x** is:

x1 =(-b + sqrt(b^2-4*a*c))/(2*a)

x2 =(-b - sqrt(b^2-4*a*c))/(2*a)

 

What if we've forgotten the formula ? Let's try to reinvent this formula by ourselves.

**1.** Subtract left and right part of the equation by **c.** We will get:

![Quadratic Equation: a*x^2+b*x+c = 0](http://storage.yvision.kz/images/user/madiyar92/YsIEUj7DQqP93z3mx7i00D546d14o0.png)

**2.** Divide both parts by **a.**

**

![Quadratic Equation: a*x^2+b*x+c = 0](http://im9.asset.yvimg.kz/userimages/madiyar92/3rG70gvTprdsa48ELCNwCkg20rcILI.png)

**

**3. (x+y)^2 = x^2 + 2*x*y + y^2**. Let's try to transform left part to (x+y)^2.

To be able to do that, add b/(2*a) to both parts of the equation:

![Quadratic Equation: a*x^2+b*x+c = 0](http://storage.yvision.kz/images/user/madiyar92/N8jN77M7JG0FmD6I2o0d31h3Pz045F.png)

**4.** Open the brackets.

![Quadratic Equation: a*x^2+b*x+c = 0](http://storage.yvision.kz/images/user/madiyar92/lo9yvd4Vq9bSIubXpNjeAojTPlV82c.png)

**5.** Simplify left part to a form **(x+y)^2**, and make denominators of the right part of the equation the same.

![Quadratic Equation: a*x^2+b*x+c = 0](http://storage.yvision.kz/images/user/madiyar92/G5Vc6SU4JbSQtRM5LC8Qaezku3wJ0J.png)

**6.** Right part can be simplified to:

![Quadratic Equation: a*x^2+b*x+c = 0](http://storage.yvision.kz/images/user/madiyar92/oXuC1Qkstbt0rFNakpy2rLdrsxOiJa.png)

**7.** Take the square root of both part:

**

![Quadratic Equation: a*x^2+b*x+c = 0](http://storage.yvision.kz/images/user/madiyar92/BR3kx5fuk2aox3kSwz6lkl57qEiCOx.png)

**

Why +-sqrt(b^2-4*a*c) ? because (-3)^2 = 9 and 3^2 = 9, that's why :).

 

**8.** Subtract **b/(2*a)** from both parts:

**

![Quadratic Equation: a*x^2+b*x+c = 0](http://storage.yvision.kz/images/user/madiyar92/77Lz2xWNwgwwL41Tqq91eMvcYVT3U8.png)

**

**9.** The final answer is:

**

![Quadratic Equation: a*x^2+b*x+c = 0](http://storage.yvision.kz/images/user/madiyar92/u523r2uO5Id36q2ZaktMRl3BQ4T6Fa.png)

**

**The End.**

---

Source: [https://yvision.kz/post/quadratic-equation-a-x-2-b-x-c-0-623232](https://yvision.kz/post/quadratic-equation-a-x-2-b-x-c-0-623232)