November 24, 2022

Quadratic Equation Formula, Examples

If you going to try to work on quadratic equations, we are enthusiastic about your adventure in math! This is really where the amusing part begins!

The information can look enormous at first. Despite that, offer yourself some grace and room so there’s no pressure or strain when figuring out these problems. To be competent at quadratic equations like a professional, you will need understanding, patience, and a sense of humor.

Now, let’s begin learning!

What Is the Quadratic Equation?

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

Although it may look similar to an abstract theory, it is simply an algebraic equation stated like a linear equation. It usually has two solutions and utilizes complicated roots to solve them, one positive root and one negative, using the quadratic equation. Solving both the roots should equal zero.

Definition of a Quadratic Equation

Foremost, remember that a quadratic expression is a polynomial equation that includes 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 figure out x if we plug these variables into the quadratic formula! (We’ll subsequently check it.)

All quadratic equations can be scripted like this, that results in solving them simply, comparatively speaking.

Example of a quadratic equation

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

x2 + 5x + 6 = 0

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

Usually, you can see these kinds of formulas when measuring a parabola, which is a U-shaped curve that can be plotted 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 working them out.

How to Work on a Quadratic Equation Utilizing the Quadratic Formula

While quadratic equations may appear greatly complicated initially, they can be cut down into several easy steps utilizing a simple formula. The formula for working out quadratic equations includes creating the equal terms and applying rudimental algebraic functions like multiplication and division to achieve 2 answers.

After all functions have been performed, we can work out the values of the variable. The answer take us one step nearer to work out the answer to our original problem.

Steps to Solving a Quadratic Equation Employing the Quadratic Formula

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

ax2 + bx + c=0

Ahead of solving anything, keep in mind to isolate the variables on one side of the equation. Here are the 3 steps to work on a quadratic equation.

Step 1: Write the equation in standard mode.

If there are variables on either side of the equation, total all equivalent terms on one side, so the left-hand side of the equation totals 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 must be factored, ordinarily utilizing the perfect square process. If it isn’t workable, put the variables in the quadratic formula, that will be your best friend for solving quadratic equations. The quadratic formula appears something like this:


Every terms responds to the equivalent terms in a conventional form of a quadratic equation. You’ll be utilizing this a great deal, so it is wise to memorize it.

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

Now once you possess 2 terms equivalent to zero, work on them to get 2 answers for x. We have 2 results 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, simplify and place it in the conventional form.

x2 + 4x - 5 = 0

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




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



We work on the second-degree equation to get:



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

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

x = 1 x = -5

After that, you have your solution! You can check your solution by checking these terms with the original equation.

12 + (4*1) - 5 = 0

1 + 4 - 5 = 0


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

25 - 20 - 5 = 0

This is it! You've figured out your first quadratic equation utilizing the quadratic formula! Congrats!

Example 2

Let's work on another example.

3x2 + 13x = 10

Initially, place it in the standard form so it is equivalent zero.

3x2 + 13x - 10 = 0

To solve this, we will put in the numbers like this:

a = 3

b = 13

c = -10

Work out x using the quadratic formula!



Let’s simplify this as far as possible by working it out exactly like we executed in the last example. Work 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 result! 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 solve quadratic equations like a professional with some practice and patience!

With this synopsis of quadratic equations and their fundamental formula, kids can now go head on against this challenging topic with assurance. By beginning with this straightforward definitions, learners acquire a solid foundation before taking on further complicated theories ahead in their academics.

Grade Potential Can Help You with the Quadratic Equation

If you are battling to understand these ideas, you may need a mathematics instructor to help you. It is better to ask for guidance before you fall behind.

With Grade Potential, you can learn all the tips and tricks to ace your subsequent mathematics examination. Turn into a confident quadratic equation problem solver so you are ready for the following complicated theories in your math studies.