November 24, 2022

Quadratic Equation Formula, Examples

If this is your first try to work on quadratic equations, we are thrilled regarding your adventure in mathematics! This is indeed where the amusing part begins!

The information can appear enormous at first. However, give yourself some grace and space so there’s no pressure or stress while figuring out these problems. To be efficient at quadratic equations like a pro, you will require patience, understanding, and a sense of humor.

Now, let’s begin learning!

What Is the Quadratic Equation?

At its core, a quadratic equation is a math equation that states distinct scenarios in which the rate of deviation is quadratic or relative to the square of few variable.

Though it might appear similar to an abstract idea, it is just an algebraic equation described like a linear equation. It ordinarily has two solutions and uses complicated roots to solve them, one positive root and one negative, through the quadratic formula. Solving both the roots should equal zero.

Definition of a Quadratic Equation

Primarily, keep in mind 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 employ this equation to work out x if we replace these variables into the quadratic formula! (We’ll look at it next.)

Any quadratic equations can be written like this, which makes working them out simply, comparatively speaking.

Example of a quadratic equation

Let’s contrast the given equation to the subsequent formula:

x2 + 5x + 6 = 0

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

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

Now that we learned what quadratic equations are and what they look like, let’s move on to solving them.

How to Work on a Quadratic Equation Using the Quadratic Formula

Even though quadratic equations might seem greatly complicated initially, they can be cut down into few easy steps utilizing a straightforward formula. The formula for solving quadratic equations includes setting the equal terms and using rudimental algebraic functions like multiplication and division to get 2 answers.

Once all functions have been carried out, we can work out the numbers of the variable. The results take us one step nearer to discover solutions to our first question.

Steps to Figuring out a Quadratic Equation Using the Quadratic Formula

Let’s promptly plug in the common quadratic equation once more so we don’t forget what it looks like

ax2 + bx + c=0

Before figuring out anything, keep in mind to detach the variables on one side of the equation. Here are the 3 steps to figuring out a quadratic equation.

Step 1: Note the equation in standard mode.

If there are terms on either side of the equation, sum all similar terms on one side, so the left-hand side of the equation totals to zero, just like the conventional model of a quadratic equation.

Step 2: Factor the equation if workable

The standard equation you will conclude with must be factored, generally through the perfect square method. If it isn’t workable, put the terms in the quadratic formula, which will be your best friend for figuring out quadratic equations. The quadratic formula appears something like this:


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

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

Now once you possess two terms equal to zero, figure out them to get 2 answers for x. We have two results due to the fact that the solution for a square root can either be positive or negative.

Example 1

2x2 + 4x - x2 = 5

At the moment, let’s fragment down this equation. Primarily, simplify and put it in the conventional form.

x2 + 4x - 5 = 0

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




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



We work on the second-degree equation to get:



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

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

x = 1 x = -5

Next, you have your solution! You can review your work by using 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 using the quadratic formula! Congrats!

Example 2

Let's check out one more example.

3x2 + 13x = 10

First, put it in the standard form so it is equivalent zero.

3x2 + 13x - 10 = 0

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

a = 3

b = 13

c = -10

figure out x employing the quadratic formula!



Let’s clarify this as far as possible by working it out just like we executed in the prior example. Work out all simple equations step by step.



You can figure 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 solution! You can revise your work utilizing 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 work out quadratic equations like nobody’s business with little practice and patience!

Granted this summary of quadratic equations and their basic formula, kids can now go head on against this complex topic with confidence. By beginning with this easy definitions, kids gain a strong understanding before moving on to further intricate ideas ahead in their studies.

Grade Potential Can Guide You with the Quadratic Equation

If you are fighting to understand these ideas, you may require a mathematics tutor to help you. It is better to ask for assistance before you lag behind.

With Grade Potential, you can learn all the tips and tricks to ace your subsequent math test. Become a confident quadratic equation solver so you are ready for the following big ideas in your math studies.