The Best Quadratic Formula Calculator to Get Full Solutions

Looking for a quadratic formula calculator that does more than just showing you the final answer? Use this online calculator to solve quadratic equations in standard form!

The best part about this quadratic equations calculator is that it will also generate a full worked solution so that you can understand each step!

As a bonus, this quadratic equation solver will also describe the nature of the roots by using the discriminant.

Input the values for \(a\), \(b\), and \(c\) for a given quadratic equation to try it out now!

Quadratic Formula Calculator

Looking for more help with the quadratic formula? Use the lesson below to start mastering this important algebra tool!

What Is a Quadratic Equation?

Quadratic equations are a cornerstone of high school algebra and essential for solving problems in high school math and beyond.

A quadratic is a specific type of polynomial equation where the degree of the equation is 2. This means that the highest power on \(x\) is 2.

A quadratic equation is any equation of the following form:

\[ax^2+bx+c=0\]

Here, \(a\), \(b\), and \(c\) are called the coefficients of the quadratic equation, and \(a≠0\).

This is the standard form of a quadratic equation, where \(a\) is the quadratic coefficient.

The solutions to this equation, also called the roots of the quadratic equation, can be real numbers or complex depending on the nature of the roots. The roots of the equation are the places on the graph where the quadratic passes through (or touches) the \(x\)-axis.

How Does the Quadratic Formula Work?

The quadratic formula is:

\[ x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a} \]

This formula calculates the \(x\) values (the roots of a quadratic equation) for any given quadratic equation.

Key to understanding the quadratic formula is the discriminant, or the expression found under the square root of the quadratic formula:

\[b^2-4ac\]

The discriminant determines the nature of the roots:

If \(b^2-4ac > 0\) (ie. a positive number), the equation has real roots.
If \(b^2-4ac = 0\), there is a single solution (or a repeated root).
If \(b^2-4ac < 0\) (ie. a negative number), there are no real solutions (meaning it may have complex roots or imaginary numbers).

In this discriminant b is the coefficient on \(x\), a is the quadratic coefficient on \(x^2\), and c is the constant term.

Looking for more free online calculators like this one? Check out my trinomial factoring calculator for full detailed solutions for trinomial factoring problems!

Try It Now!

While I always recommend understanding how to use the quadratic formula, this quadratic equation calculator is the ultimate math solver for checking your work, or verifying your solution.

My hope is that this online tool is a helpful companion for tackling any equation of the form \(ax^2+bx+c=0\) that you come across!

Whether you’re a student, teacher, or just curious about the quadratic formula, my quadratic formula calculator is your go-to online tool for solving quadratic equations with ease!

Ready to take it to the next level? Check out this collection of quadratic formula word problems!

To learn more about the tools that we can use to solve quadratic equations, check out my walkthrough on how to factor quadratic trinomials!

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