November 24, 2022

Quadratic Equation Formula, Examples

If you going to try to work on quadratic equations, we are thrilled regarding your venture in mathematics! This is indeed where the most interesting things begins!

The details can appear enormous at first. Despite that, give yourself some grace and room so there’s no rush or strain when solving these questions. To be efficient at quadratic equations like a pro, you will need understanding, patience, and a sense of humor.

Now, let’s start learning!

What Is the Quadratic Equation?

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

Though it might appear similar to an abstract concept, it is simply an algebraic equation described like a linear equation. It usually has two results and utilizes intricate roots to work out them, one positive root and one negative, through the quadratic equation. Working out both the roots the answer to which will be zero.

Meaning 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 standard form is:

ax2 + bx + c

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

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

Example of a quadratic equation

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

x2 + 5x + 6 = 0

As we can observe, there are 2 variables and an independent term, and one of the variables is squared. Therefore, compared to the quadratic formula, we can confidently say this is a quadratic equation.

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

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

How to Figure out a Quadratic Equation Employing the Quadratic Formula

Even though quadratic equations might appear greatly complicated when starting, they can be cut down into multiple simple steps employing a straightforward formula. The formula for solving quadratic equations consists of setting the equal terms and applying rudimental algebraic operations like multiplication and division to achieve 2 results.

After all functions have been carried out, we can solve for the values of the variable. The answer take us another step closer to discover result to our actual problem.

Steps to Working on a Quadratic Equation Employing the Quadratic Formula

Let’s promptly put in the original quadratic equation again so we don’t forget what it seems like

ax2 + bx + c=0

Before working on anything, bear in mind to detach the variables on one side of the equation. Here are the three steps to solve a quadratic equation.

Step 1: Note the equation in standard mode.

If there are variables on either side of the equation, total all similar terms on one side, so the left-hand side of the equation is equivalent to zero, just like the standard mode of a quadratic equation.

Step 2: Factor the equation if workable

The standard equation you will end up with must be factored, ordinarily using the perfect square process. If it isn’t feasible, plug the terms in the quadratic formula, that will be your best buddy for solving quadratic equations. The quadratic formula appears something like this:


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

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

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

Example 1

2x2 + 4x - x2 = 5

Now, let’s fragment down this equation. Primarily, simplify and put it in the standard form.

x2 + 4x - 5 = 0

Immediately, let's determine the terms. If we compare these to a standard quadratic equation, we will identify the coefficients of x as ensuing:




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 simplify the square root to get two linear equations and work out:

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

x = 1 x = -5

Now, you have your answers! You can check your workings 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 worked out your first quadratic equation utilizing the quadratic formula! Congrats!

Example 2

Let's try another example.

3x2 + 13x = 10

Let’s begin, put it in the standard form so it results in zero.

3x2 + 13x - 10 = 0

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

a = 3

b = 13

c = -10

figure out x employing the quadratic formula!



Let’s streamline this as much as possible by solving it just like we performed in the previous example. Figure out all simple 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 answer! You can review your workings 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 solve quadratic equations like a professional with little practice and patience!

Granted this synopsis of quadratic equations and their rudimental formula, students can now take on this difficult topic with faith. By beginning with this simple definitions, children secure a strong foundation ahead of taking on further complicated theories down in their academics.

Grade Potential Can Guide You with the Quadratic Equation

If you are battling to get a grasp these concepts, you may require a mathematics tutor to assist you. It is best to ask for guidance before you lag behind.

With Grade Potential, you can study all the handy tricks to ace your next mathematics examination. Turn into a confident quadratic equation solver so you are ready for the ensuing complicated theories in your math studies.