## Introduction to Quadratic Formula Calculator

Quadratic Formula Calculator is an online tool that is used to **find the solution of quadratic equation root** value in a couple of seconds.

Quadratic Calculator determines the solution of the second degree of algebraic expression of a variable in the form of root values (real or imaginary).

## What is the Quadratic Formula?

Quadratic equation formula is used to **solve the quadratic equation** ax^{2}+bx+c=0 and get a solution in real or imaginary roots.

Although it implements the condition that x^{2}≠0 because it makes the quadratic equation a linear equation. Whereas x is a variable in the quadratic equation the variable may be y,z,w…etc as per the question and it does not affect the solution.

## Formula Behind Quadratic Equation Calculator

Quadratic equations consist of **variables or coefficients** as ax^{2}+bx+c=0 where a,b, and c are the coefficients and x is the variable that may vary. The formula used by Quadratic Formula Calculator to solve quadratic problems is,

$$ x \;=\; \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$

Here b^{2}-4ac is the discriminant value.

- If D
^{2}=b^{2}-4ac is zero then one root is real - If D
^{2}=b^{2}-4ac ≤0 is less than equal to zero then it gives imaginary roots - If D
^{2}=b^{2}-4ac ≥0 is greater than equal to zero then it gives real roots

## Working Process of Quadratic Calculator

Quadratic equation calculator can give the solution of a quadratic equation in the form of two roots that satisfy the given quadratic equation. Our tool provides you with solutions to quadratic equations in the simplest way with the help of quadratic formulas for a better understanding of this concept.

When the quadratic equation solver adds the **coefficients a,b, and c** in the quadratic problem, it applies the quadratic formula and adds the coefficient values to it. Then simply the these values as per the usual algebraic method.

After simplification, two factors are obtained with positive or negative sign (x ± n). Quadratic solver keeps these factors equal to zero after separating them as (x+n)=0=(x-n). Now you have **two values of x** as a solution of a quadratic equation in no time.

You can check the value of your roots by putting it on the given quadratic equation or using the quadratic formula solver. If it satisfies both sides then your solution is written or if not then you did the wrong calculation.

For 100% accuracy in the solution, you should use our quadratic function calculator that provides a solution without any error.

## Solved Example of Quadratic Problem

The Quadratic Formula Calculator can be used to solve quadratic problems but it is also important to know the manual calculations, so an example is given below

### Example:

Calculate the following using the quadratic formula:

$$ 2x^2 + 9x - 5 \;=\; 0 $$

**Solution:**

Quadratic equation in standard form

$$ ax^2 + bx + c \;=\; 0 $$

$$ 2x^2 + 9x - 5 \;=\; 0 $$

$$ a \;=\; 2, b \;=\; 9, c \;=\; -5 $$

Add the value of a,b,c in the quadratic equation formula

$$ x \;=\; \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$

$$ x \;=\; \frac{-9 \pm \sqrt{9^2 - 4 . 2 . (-5)}}{2 . 2} $$

Simplify to get the root value of x

$$ x \;=\; \frac{-9 \pm \sqrt{81 - (-40)}}{4} $$

$$ x \;=\; \frac{-9 \pm \sqrt{121}}{4} $$

$$ x \;=\; \frac{-9 \pm 11}{4} $$

$$ x \;=\; \frac{-9 + 11}{4} , x \;=\; \frac{-9 -11}{4} $$

$$ x \;=\; \frac{2}{4}, x \;=\; \frac{-20}{4} $$

$$ x \;=\; \frac{1}{2}, x \;=\; -5 $$

Put one of the x values in the given equation to check whether your roots value then it satisfies.

$$ 2x^2 + 9x - 5 \;=\; 0 $$

$$ 2 \biggr( \frac{1}{2} \biggr)^2 + 9. \frac{1}{2} - 5 \;=\; 0 $$

$$ 2 . \frac{1}{4} + 0 . \frac{1}{2} - 5 \;=\; 0 $$

$$ 2 . \frac{1}{4} + 9 . \frac{1}{2} - 5 \;=\; 0 $$

$$ \frac{1}{2} + \frac{9}{2} - 5 \;=\; 0 $$

$$ \frac{10}{2} - 5 \;=\; 0 $$

$$ 5 - 5 \;=\; 0 $$

$$ 0 = 0 $$

As you can see it satisfies the given equation which means our root value is true.

## How to Use Quadratic Formula Calculator?

The quadratic equation calculator has a simple design that allows you to solve various types of quadratic equation problems instantly. For this, you need to follow some simple steps for a better experience during quadratic formula equation calculation. These steps are:

- Enter the
**coefficient a,b,c,d value in the input field**of the quadratic equation solver. - Check your algebraic function before pressing the calculate button to get the exact solution of your input value
- Click the “Calculate” button of the quadratic calculator for the solution of Quadratic formula questions
- Click the “Recalculate” button of quadratic solver for more evaluation of the Quadratic problem
- You can use the load example for the calculation of more problems of the Quadratic equation formula

## Output from Quadratic Equation Solver

Quadratic Formula Calculator gives you a solution to your input function instantly when you click on the calculate button. It may include as:

**In the Result Box,**

You get the solution of an algebraic expression of second-degree problems

**Steps Box**

Click on the steps option so that you get the given **solution of the Quadratic equation** problem in a step-by-step method

## Benefits of Quadratic Solver

The quadratic equation calculator is an amazing tool for solving quadratic equations to get the roots values. It gives you multiple benefits whenever you use it for the evaluation of various types of quadratic equation problems. These advantages are:

- Quadratic Calculator is a
**trustworthy tool**as it always provides you with accurate solutions to Quadratic equation problems - It is a speedy tool that evaluates the Quadratic equation formula problems in a couple of seconds without making any mankind error in the solution.
- A quadratic equation solver is a free tool that allows you to use it for the calculation of root values without any fee.
- A quadratic formula solver is used for practice to solve algebraic equations of second-degree root problems.
- Quadratic function calculator has a simple design anyone or even a
**beginner can easily use**it for the solution of quadratic equations. - You can operate the Quadratic Formula Calculator on a desktop, mobile, or laptop.