November 24, 2022

Quadratic Equation Formula, Examples

If this is your first try to solve quadratic equations, we are excited regarding your adventure in math! This is actually where the amusing part starts!

The details can appear too much at first. Despite that, give yourself some grace and room so there’s no rush or strain while working through these questions. To be efficient at quadratic equations like an expert, you will need patience, understanding, and a sense of humor.

Now, let’s start learning!

What Is the Quadratic Equation?

At its center, a quadratic equation is a math equation that describes different scenarios in which the rate of deviation is quadratic or relative to the square of few variable.

Though it may look like an abstract concept, it is just an algebraic equation expressed like a linear equation. It usually has two answers 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.

Meaning 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 use this formula to figure out x if we replace these variables into the quadratic equation! (We’ll go through it later.)

All quadratic equations can be scripted like this, which makes solving them easy, comparatively speaking.

Example of a quadratic equation

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

x2 + 5x + 6 = 0

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

Usually, you can see these types of formulas when scaling a parabola, which is a U-shaped curve that can be graphed on an XY axis with the information that a quadratic equation gives us.

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

How to Solve a Quadratic Equation Employing the Quadratic Formula

Even though quadratic equations may appear greatly complicated initially, they can be cut down into multiple easy steps utilizing a straightforward formula. The formula for solving quadratic equations involves creating the equal terms and using basic algebraic operations like multiplication and division to obtain two answers.

After all operations have been carried out, we can figure out the units of the variable. The answer take us another step nearer to work out the result to our actual problem.

Steps to Figuring out a Quadratic Equation Employing the Quadratic Formula

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

ax2 + bx + c=0

Ahead of figuring out anything, keep in mind to isolate 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 conventional mode.

If there are variables on both sides of the equation, add all alike terms on one side, so the left-hand side of the equation totals to zero, just like the standard mode of a quadratic equation.

Step 2: Factor the equation if possible

The standard equation you will wind up with should be factored, generally through the perfect square method. If it isn’t workable, plug the variables in the quadratic formula, which will be your closest friend for working out quadratic equations. The quadratic formula appears like this:


Every terms responds to the identical terms in a conventional form of a quadratic equation. You’ll be using this a lot, so it pays to remember it.

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

Now that you have two terms equivalent to zero, figure out them to obtain 2 solutions for x. We have two answers due to the fact that the answer for a square root can either be negative or positive.

Example 1

2x2 + 4x - x2 = 5

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

x2 + 4x - 5 = 0

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




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



We work on the second-degree equation to achieve:



Now, let’s simplify the square root to attain two linear equations and solve:

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

x = 1 x = -5

Next, you have your solution! You can review your workings 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

This is it! You've solved your first quadratic equation utilizing the quadratic formula! Congratulations!

Example 2

Let's check out one more example.

3x2 + 13x = 10

Let’s begin, place it in the standard form so it results in 0.

3x2 + 13x - 10 = 0

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

a = 3

b = 13

c = -10

figure out 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. Work out all easy equations step by step.



You can work out 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 answer! You can check your workings through 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 a pro with some practice and patience!

With this synopsis of quadratic equations and their basic formula, children can now tackle this challenging topic with faith. By starting with this easy explanation, children secure a firm grasp prior taking on more complicated theories down in their studies.

Grade Potential Can Help You with the Quadratic Equation

If you are struggling to understand these ideas, you might require a mathematics instructor 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 problem solver so you are prepared for the ensuing intricate theories in your mathematical studies.