## Solve quadratic equations step by step

The calculator will solve the quadratic equation step by step either by completing the square or using the quadratic formula. It will find both the real and the imaginary (complex) roots.

Related calculator: Discriminant Calculator

For example, x^2+4x+3=0 or x^2+4=5x.

Choose a method:

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Welcome to the ultimate online Quadratic Equation Calculator! Our tool helps you solve quadratic equations with ease, giving you the most accurate results using the quadratic formula.

## How to Use the Quadratic Equation Calculator?

• ### Input

Enter the given quadratic equation and choose the method for solving it.

• ### Calculation

After entering the equation, click the "Calculate" button. The calculator will quickly determine the solutions of the equation.

• ### Result

In a short moment, the calculator will show the roots. A quadratic equation can have one of three types of roots: two distinct real roots, one repeated real root, or two complex roots.

## What Is a Quadratic Equation?

A quadratic equation is a particular type of polynomial equation of the second degree. It has the following form:

$$ax^2+bx+c=0,$$

where:

• $x$ is the variable or the unknown we aim to find.
• $a$, $b$ and $c$ are some constants.
• It's essential that $a\ne0$, otherwise, the equation will not be quadratic but linear.

The graphical representation of a quadratic function is a parabola. Depending on the values of $a$, $b$, and $c$, the parabola can open upwards or downwards and have its vertex anywhere in the coordinate plane.

The quadratic formula is a universal method to find the roots or solutions of any quadratic equation. It is expressed as:

$$x_{1,2}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$$

The term inside the square root is called the discriminant. It determines the nature of the roots:

• If $b^2-4ac\gt0$, the equation has two distinct real roots.
• If $b^2-4ac=0$, there's one real root (a repeated root).
• If $b^2-4ac\lt0$, the equation has two complex roots.

## Why Choose Our Quadratic Equation Calculator?

• ### Accuracy and Precision

Our calculator is equipped with advanced algorithms that ensure the results are accurate every time. Whether your equation has real or complex roots, our tool delivers the correct solution.

• ### User-Friendly Interface

We've developed a simple and intuitive interface that even those new to quadratic equations can easily navigate.

• ### Instant Results

Time is invaluable. Our calculator provides immediate solutions, allowing users to quickly move on to other tasks or verify their manual calculations without delay.

### FAQ

#### Can the calculator handle fractional or decimal coefficients?

Yes, our Quadratic Equation Calculator is designed to work with both whole numbers and decimals or fractions. Just input the coefficients as they appear in the provided field.

#### Does the calculator explain the step-by-step process of finding the roots?

Our calculator offers a comprehensive breakdown, explaining each step taken to derive the solution using the quadratic formula.

#### Does the calculator provide a graphical representation of the quadratic equation?

No, it doesn't provide it.

#### What is the Quadratic Equation Calculator?

The Quadratic Equation Calculator is an online tool designed to solve quadratic equations. By inputting the equation, users can find out its roots instantly.