November 24, 2022

Quadratic Equation Formula, Examples

If this is your first try to figure out quadratic equations, we are excited regarding your adventure in math! This is really where the most interesting things begins!

The data can appear overwhelming at first. Despite that, offer yourself some grace and room so there’s no pressure or stress when solving these questions. To be competent at quadratic equations like an expert, you will require patience, understanding, and a sense of humor.

Now, let’s start learning!

What Is the Quadratic Equation?

At its heart, a quadratic equation is a math equation that describes various scenarios in which the rate of change is quadratic or relative to the square of some variable.

Though it may look similar to an abstract concept, it is simply an algebraic equation stated like a linear equation. It ordinarily has two answers and uses intricate roots to solve them, one positive root and one negative, through the quadratic equation. Solving both the roots the answer to which will be zero.

Definition of a Quadratic Equation

Foremost, keep in mind that a quadratic expression is a polynomial equation that includes a quadratic function. It is a second-degree equation, and its usual form is:

ax2 + bx + c

Where “a,” “b,” and “c” are variables. We can employ this formula to work out x if we replace these terms into the quadratic equation! (We’ll subsequently check it.)

All quadratic equations can be written like this, which makes solving them easy, relatively speaking.

Example of a quadratic equation

Let’s contrast the ensuing equation to the previous formula:

x2 + 5x + 6 = 0

As we can observe, there are two variables and an independent term, and one of the variables is squared. Consequently, compared to the quadratic formula, we can surely state this is a quadratic equation.

Commonly, you can find these kinds of equations when scaling 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 know what quadratic equations are and what they appear like, let’s move on to figuring them out.

How to Work on a Quadratic Equation Using the Quadratic Formula

Although quadratic equations might look greatly complicated when starting, they can be divided into several easy steps employing an easy formula. The formula for figuring out quadratic equations involves setting the equal terms and using rudimental algebraic functions like multiplication and division to get 2 answers.

Once all operations have been performed, we can figure out the units of the variable. The solution take us one step nearer to discover answer to our actual question.

Steps to Solving a Quadratic Equation Utilizing the Quadratic Formula

Let’s quickly place in the general quadratic equation again so we don’t overlook what it looks like

ax2 + bx + c=0

Prior to figuring out anything, keep in mind to detach the variables on one side of the equation. Here are the three steps to work on a quadratic equation.

Step 1: Note the equation in conventional mode.

If there are terms on either side of the equation, add all similar terms on one side, so the left-hand side of the equation equals zero, just like the standard model of a quadratic equation.

Step 2: Factor the equation if workable

The standard equation you will wind up with should be factored, ordinarily using the perfect square process. If it isn’t workable, put the variables in the quadratic formula, which will be your best buddy for working out quadratic equations. The quadratic formula appears similar to this:


Every terms correspond to the same terms in a conventional form of a quadratic equation. You’ll be using this significantly, so it pays to remember it.

Step 3: Apply the zero product rule and solve the linear equation to discard possibilities.

Now that you have 2 terms resulting in zero, figure out them to get two answers for x. We get two answers because the answer for a square root can either be positive or negative.

Example 1

2x2 + 4x - x2 = 5

At the moment, let’s piece down this equation. First, streamline and put it in the standard form.

x2 + 4x - 5 = 0

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




To solve quadratic equations, let's plug this into the quadratic formula and work out “+/-” to involve each square root.



We work on the second-degree equation to achieve:



After this, let’s clarify the square root to obtain two linear equations and solve:

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 initial 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! Congratulations!

Example 2

Let's check out another example.

3x2 + 13x = 10

First, put it in the standard form so it results in zero.

3x2 + 13x - 10 = 0

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

a = 3

b = 13

c = -10

Work out x using the quadratic formula!



Let’s streamline this as far as workable by solving it just like we executed in the prior example. Solve all simple equations step by step.



You can work out x by taking the positive and negative square roots.

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

x=46 x=-306

x=23 x=-5

Now, you have your result! You can check your workings 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 this is it! You will solve quadratic equations like a pro with little patience and practice!

Granted this summary of quadratic equations and their basic formula, students can now go head on against this complex topic with confidence. By starting with this easy definitions, kids secure a strong grasp prior undertaking further complicated ideas later in their academics.

Grade Potential Can Guide You with the Quadratic Equation

If you are struggling to understand these theories, you might need a mathematics tutor to assist you. It is better to ask for guidance before you get behind.

With Grade Potential, you can learn all the tips and tricks to ace your subsequent mathematics examination. Become a confident quadratic equation solver so you are prepared for the ensuing intricate theories in your math studies.