The quadratic formula calculator helps you to find the roots of the quadratic equation and shows step-by-step calculations. Our free online tool gives explicit results by optimizing the use of resources.

Our quadratic equation solver helps you to reduce the following second-degree expression to its roots:

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

Where,

• x is the unknown value
• a, b is the quadratic coefficient, a ≠ 0
• c is a constant

$$\dfrac{a}{a}x^2 + \dfrac{b}{a}x + \dfrac{c}{a} = 0$$

$$x^2 + \dfrac{b}{a}x + \dfrac{c}{a} = 0$$

$$x^2 + \dfrac{b}{a}x = -\dfrac{c}{a}$$

Add $$(\frac{b}{2a})^2$$ on both sides of the equation.

$$x^2 + \dfrac{b}{a}x + (\dfrac{b}{2a})^2 = -\dfrac{c}{a} + (\dfrac{b}{2a})^2$$

$$(x + \dfrac{b}{2a})^2 = -\dfrac{c}{a} + \dfrac{b^2}{4a^2}$$

$$(x + \dfrac{b}{2a})^2 = \dfrac{b^2 – 4ac}{4a^2}$$

Take a square root on both sides of the equation.

$$\sqrt{(x + \dfrac{b}{2a})^2} = \pm \sqrt{\dfrac{b^2 – 4ac}{4a^2}}$$

$$x + \dfrac{b}{2a} = \pm \dfrac{\sqrt{b^2 – 4ac}}{2a}$$

$$x = -\dfrac{b}{2a} \pm \dfrac{\sqrt{b^2 – 4ac}}{2a}$$

$$x = \dfrac{-b \pm \sqrt{b^2 – 4ac}}{2a}$$

## How To Use Quadratic Formula?

The quadratic formula calculator helps you to solve any quadratic equation in a matter of seconds. However, if your goal comes up with the manual calculations, you must delve into the example to explore more.

### Example:

Suppose that we have 3x^2 - 5x + 2 = 0. We need to solve by the quadratic equation formula.

#### Solution:

$$x = \dfrac{-b \pm \sqrt{b^2 – 4ac}}{2a}$$

And we also know the values of a, b, and c in the above-given statement:

a= 3, b= -5, and c= 2

Put the values in the formula.

$$x = \dfrac{-5 \pm \sqrt{-5^2 – 4(3)(2)}}{2(3)}$$

$$x = \dfrac{5 \pm \sqrt{25 – 24)}}{6}$$

$$x = \dfrac{5 \pm \sqrt{1}}{6}$$

Here the roots of a quadratic equation have two solutions.

Root # 1

$$x = \dfrac{5+1}{6}$$

$$x =\dfrac{6}{6}$$

$$x = 1$$

Root # 2

$$x = \dfrac{5-1}{6}$$

$$x = \dfrac{4}{6}$$

$$x = \dfrac{2}{3}$$

## Working of Quadratic Formula Calculator:

The quadratic root calculator will help you carry out calculations easily! Just enter the required values. Our quadratic function calculator will work best for you!

Input:

• Choose equation form
• Choose computation method
• Put the values of a, b, and c in the respective field
• Press the “Calculate” button

Output:

• Quadratic formula solver will give you an instant answer with the steps and graph shown

## FAQs:

### How Many Possibilities Does a Quadratic Equation Have?

There are three possibilities which include:

• If the discriminant is positive, then there are 2 solutions
• If the discriminant is negative, then there is no solution
• If the discriminant equals 0, then there is 1 solution

### Can a Quadratic Formula be Used for Everything?

No, It is just used to solve the quadratic equations that are in the form of $$ax^2 + bx + c = 0$$. This form is also known as the standard form of the quadratic formula calculator.

### How Many Roots Does a Quadratic Formula Equation Have?

A second-degree equation formula equation has two roots. It depends on the degree of the equation.