November 24, 2022

Quadratic Equation Formula, Examples

If you’re starting to work on quadratic equations, we are enthusiastic about your adventure in mathematics! This is really where the fun begins!

The data can appear enormous at start. Despite that, give yourself some grace and room so there’s no hurry or strain while figuring out these questions. To be efficient at quadratic equations like an expert, you will need understanding, patience, and a sense of humor.

Now, let’s start learning!

What Is the Quadratic Equation?

At its core, a quadratic equation is a arithmetic equation that states various situations in which the rate of change is quadratic or proportional to the square of some variable.

Though it may look similar to an abstract theory, it is simply an algebraic equation described like a linear equation. It ordinarily has two results and utilizes complicated roots to solve them, one positive root and one negative, through the quadratic formula. Working out both the roots the answer to which will be zero.

Meaning of a Quadratic Equation

Foremost, remember that a quadratic expression is a polynomial equation that comprises of a quadratic function. It is a second-degree equation, and its standard form is:

ax2 + bx + c

Where “a,” “b,” and “c” are variables. We can use this equation to solve for x if we plug these variables into the quadratic formula! (We’ll go through it later.)

Ever quadratic equations can be written like this, that makes working them out simply, relatively speaking.

Example of a quadratic equation

Let’s compare the following equation to the subsequent equation:

x2 + 5x + 6 = 0

As we can observe, there are 2 variables and an independent term, and one of the variables is squared. Consequently, linked to the quadratic formula, we can confidently tell this is a quadratic equation.

Generally, you can observe these types of formulas when measuring a parabola, which is a U-shaped curve that can be plotted on an XY axis with the information that a quadratic equation gives us.

Now that we learned what quadratic equations are and what they appear like, let’s move ahead to working them out.

How to Work on a Quadratic Equation Utilizing the Quadratic Formula

While quadratic equations might seem greatly complicated when starting, they can be divided into few simple steps using an easy formula. The formula for working out quadratic equations includes creating the equal terms and using basic algebraic functions like multiplication and division to get 2 results.

After all operations have been executed, we can solve for the units of the variable. The results take us one step nearer to find solutions to our actual question.

Steps to Figuring out a Quadratic Equation Employing the Quadratic Formula

Let’s quickly plug in the common quadratic equation again so we don’t forget what it looks like

ax2 + bx + c=0

Ahead of solving anything, keep in mind to separate the variables on one side of the equation. Here are the three steps to figuring out a quadratic equation.

Step 1: Note the equation in conventional mode.

If there are terms on both sides of the equation, add all equivalent terms on one side, so the left-hand side of the equation is equivalent to zero, just like the conventional mode of a quadratic equation.

Step 2: Factor the equation if workable

The standard equation you will conclude with must be factored, usually using the perfect square process. If it isn’t workable, plug the terms in the quadratic formula, that will be your closest friend for figuring out quadratic equations. The quadratic formula seems something like this:


All the terms coincide to the equivalent terms in a standard form of a quadratic equation. You’ll be utilizing this significantly, so it is wise to memorize it.

Step 3: Apply the zero product rule and figure out the linear equation to eliminate possibilities.

Now once you have two terms equivalent to zero, solve them to achieve two solutions for x. We have two answers because the solution for a square root can either be positive or negative.

Example 1

2x2 + 4x - x2 = 5

Now, let’s piece down this equation. Primarily, clarify and place it in the conventional form.

x2 + 4x - 5 = 0

Now, let's identify the terms. If we contrast these to a standard quadratic equation, we will find the coefficients of x as follows:




To work out quadratic equations, let's put this into the quadratic formula and find the solution “+/-” to include both square root.



We solve the second-degree equation to get:



Next, let’s streamline the square root to attain two linear equations and work out:

x=-4+62 x=-4-62

x = 1 x = -5

Next, you have your result! You can check your solution by checking these terms with the first equation.

12 + (4*1) - 5 = 0

1 + 4 - 5 = 0


-52 + (4*-5) - 5 = 0

25 - 20 - 5 = 0

That's it! You've solved your first quadratic equation utilizing the quadratic formula! Congrats!

Example 2

Let's check out another example.

3x2 + 13x = 10

Initially, place it in the standard form so it equals zero.

3x2 + 13x - 10 = 0

To figure out this, we will plug in the numbers like this:

a = 3

b = 13

c = -10

figure out x employing the quadratic formula!



Let’s streamline this as far as possible by figuring it out exactly like we did in the prior example. Solve all simple equations step by step.



You can solve for x by considering the negative and positive square roots.

x=-13+176 x=-13-176

x=46 x=-306

x=23 x=-5

Now, you have your answer! You can review your work using substitution.

3*(2/3)2 + (13*2/3) - 10 = 0

4/3 + 26/3 - 10 = 0

30/3 - 10 = 0

10 - 10 = 0


3*-52 + (13*-5) - 10 = 0

75 - 65 - 10 =0

And that's it! You will solve quadratic equations like a pro with little practice and patience!

With this overview of quadratic equations and their rudimental formula, kids can now tackle this difficult topic with assurance. By beginning with this straightforward explanation, children acquire a strong grasp before undertaking more complicated concepts later in their studies.

Grade Potential Can Assist You with the Quadratic Equation

If you are struggling to get a grasp these concepts, you might need a mathematics teacher to help you. It is better to ask for guidance before you fall behind.

With Grade Potential, you can learn all the helpful hints to ace your next math exam. Turn into a confident quadratic equation solver so you are prepared for the following intricate ideas in your math studies.