November 24, 2022

Quadratic Equation Formula, Examples

If you going to try to solve quadratic equations, we are enthusiastic regarding your venture in math! This is really where the fun begins!

The details can appear too much at start. Despite that, offer yourself a bit of grace and room so there’s no hurry or stress when working through these questions. To be efficient at quadratic equations like an expert, you will need a good sense of humor, patience, and good understanding.

Now, let’s begin learning!

What Is the Quadratic Equation?

At its center, a quadratic equation is a mathematical equation that states different scenarios in which the rate of deviation is quadratic or proportional to the square of few variable.

Though it seems similar to an abstract theory, it is just an algebraic equation stated like a linear equation. It generally has two results and utilizes complicated roots to figure out them, one positive root and one negative, through the quadratic formula. Working out both the roots will be equal to zero.

Definition of a Quadratic Equation

Primarily, keep in mind that a quadratic expression is a polynomial equation that consist of a quadratic function. It is a second-degree equation, and its conventional form is:

ax2 + bx + c

Where “a,” “b,” and “c” are variables. We can utilize this formula to work out x if we put these terms into the quadratic equation! (We’ll get to that later.)

Ever quadratic equations can be scripted like this, which makes figuring them out simply, relatively speaking.

Example of a quadratic equation

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

x2 + 5x + 6 = 0

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

Usually, you can see these kinds of equations when scaling a parabola, that is a U-shaped curve that can be plotted on an XY axis with the details that a quadratic equation gives us.

Now that we understand what quadratic equations are and what they look like, let’s move forward to working them out.

How to Figure out a Quadratic Equation Using the Quadratic Formula

While quadratic equations might look very complicated when starting, they can be broken down into several simple steps using a simple formula. The formula for solving quadratic equations involves setting the equal terms and using rudimental algebraic operations like multiplication and division to get two answers.

Once all operations have been carried out, we can work out the numbers of the variable. The results take us single step nearer to work out the answer to our first question.

Steps to Figuring out a Quadratic Equation Using the Quadratic Formula

Let’s quickly plug in the general quadratic equation once more so we don’t overlook what it looks like

ax2 + bx + c=0

Ahead of solving anything, remember to detach the variables on one side of the equation. Here are the 3 steps to figuring out a quadratic equation.

Step 1: Write the equation in standard mode.

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

Step 2: Factor the equation if feasible

The standard equation you will conclude with should be factored, ordinarily using the perfect square process. If it isn’t possible, plug the terms in the quadratic formula, which will be your best friend for figuring out quadratic equations. The quadratic formula seems something like this:


Every terms responds to the same terms in a standard form of a quadratic equation. You’ll be employing this significantly, so it is wise to remember it.

Step 3: Implement the zero product rule and figure out the linear equation to remove possibilities.

Now once you have two terms resulting in zero, solve them to attain two answers for x. We get 2 answers due to the fact that the answer for a square root can either be positive or negative.

Example 1

2x2 + 4x - x2 = 5

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

x2 + 4x - 5 = 0

Now, let's recognize the terms. If we contrast these to a standard quadratic equation, we will get the coefficients of x as ensuing:




To solve quadratic equations, let's replace this into the quadratic formula and find the solution “+/-” to involve both square root.



We solve the second-degree equation to get:



After this, let’s simplify the square root to achieve two linear equations and figure out:

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

x = 1 x = -5

Next, you have your solution! You can revise 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 worked out your first quadratic equation using the quadratic formula! Congrats!

Example 2

Let's try another example.

3x2 + 13x = 10

Let’s begin, place it in the standard form so it equals zero.

3x2 + 13x - 10 = 0

To work on this, we will plug in the values like this:

a = 3

b = 13

c = -10

Solve for x utilizing the quadratic formula!



Let’s streamline this as far as possible by figuring it out exactly like we performed in the previous example. Figure out all easy equations step by step.



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

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

x=46 x=-306

x=23 x=-5

Now, you have your solution! 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 nobody’s business with some practice and patience!

Granted this synopsis of quadratic equations and their rudimental formula, kids can now go head on against this challenging topic with confidence. By opening with this easy explanation, children gain a strong foundation ahead of moving on to more intricate theories ahead in their academics.

Grade Potential Can Assist You with the Quadratic Equation

If you are battling to get a grasp these ideas, you may need a mathematics teacher to help you. It is better to ask for assistance before you get behind.

With Grade Potential, you can understand all the handy tricks to ace your subsequent math test. Become a confident quadratic equation problem solver so you are prepared for the ensuing complicated theories in your mathematics studies.