Algebra is one of the important parts of mathematics, and it is right to say it is an essential branch of mathematics. Algebra includes three common parts in their equation such as unknown parts which are known as variable, coefficient and number values. According to the degree available in the unknown part, the algebra is known as a different name such as a linear equation, polynomial equation, quadratic equation, cubic equation, exponential equation and much more. Thus, the algebra is a large part of mathematics. Here we are going to learn solving quadratic equations in different methods.

**About quadratic equation**

It is one of the algebraic equation which includes two factors or roots of unknown value. If learn simply, the standard format of quadratic equation is-

ax² + bx + c = 0

Here the standard format of a quadratic equation is visible where you can find variable (x), constant or number term (c) and coefficient of x² and x i.e. a and b.

Now solving the quadratic equation is quite simple with the latest algebra calculators but slightly difficult if solved by formula methods. Different methods you can use to solve the quadratic equations in which formula method is explained below in the content.

Consider an example to learn how to solve quadratic equation by formula method

x² + 3x – 4 = 0

Formula to identify the unknown term is: -b ± √b²-4ac⁄2a

According to the standard format of quadratic equation a = 1, b = 3 and c = -4

Put these values on the formula to find the value of a variable. You will get,

x = -3 ± √9 – 4.1. (-4)⁄2.1

x = -3 ± √9+16⁄2

x = -3 ± √25⁄2

x = -3 ± 5⁄2

Now, you can consider mathematical signs separately to identify both values separately that can balance the whole equation. Follow steps given below-

x = -3 + 5⁄2

x = 2⁄2

x = 1

And,

x = – 3 – 5⁄2

x = – 8⁄2

x = – 4

Now, you have two separate values of variable, i.e. x=1 and-4

This is formula method to solve any quadratic equation. It is quite simple, but you have to perform a much mathematical operation like multiplication, division, subtraction, and addition too. Also, you use other methods for solving a quadratic equation. In the quadratic equation, there are two roots are available that can balance the whole equation. Consider the same example to learn the root method of **solving quadratic equations**. x² + 3x – 4 = 0

Here a = 1, b = 3 and c = – 4

To find out the variable values, use particular formula as-

α + β = – b⁄a

α β = c⁄a

Put the values to get the values of α and β

α + β = – 3⁄1

α + β = – 3

And

α β = -4⁄1

α β = – 4

Square both the term of ∝+β to find out unknown values as

α² + β² + 2αβ = 9

Now,

(α – β) ² + 2αβ + 22 αβ = 9

(α – β) ² + 2αβ + 22αβ = 9

(α – β) ² + 4αβ = 9

Put the values of α β in the above equation

(α – β) ² + 4 * – 4 = 9

(α – β) ² – 16 = 9

(α – β) ² = 25

α – β = 5

Now add α – β and α + β

You will get

2α = 2

Then

α = 1

Put the value of ∝ in any above equation

You will get

β = -4

Hence, you have a choice to use different methods to solve a quadratic equation. On the other hand, you can choose the algebra calculator that can easily find out variable values and deliver results in fast. In the algebra calculator, you just need to enter the quadratic equitation on the required field in the calculator. Thus, enter one next tap to solve the equation. The calculator solves the equation with the genuine method, and there is no short answer you will get. Thus, solving quadratic equations is quite easy with the calculator.