November 24, 2022

Quadratic Equation Formula, Examples

If you’re starting to figure out quadratic equations, we are excited about your journey in math! This is really where the amusing part begins!

The details can appear enormous at start. However, give yourself some grace and room so there’s no rush or stress while figuring out these problems. To be efficient at quadratic equations like an expert, you will require a good sense of humor, patience, and good understanding.

Now, let’s start learning!

What Is the Quadratic Equation?

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

Although it might appear like an abstract theory, it is just an algebraic equation described like a linear equation. It usually has two answers and uses intricate roots to solve them, one positive root and one negative, using the quadratic equation. Working out both the roots should equal zero.

Definition of a Quadratic Equation

Primarily, bear in mind 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 employ this formula to work out x if we replace these variables into the quadratic formula! (We’ll get to that later.)

Ever quadratic equations can be written like this, which makes solving them easy, comparatively speaking.

Example of a quadratic equation

Let’s compare the ensuing equation to the last equation:

x2 + 5x + 6 = 0

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

Usually, you can observe these types of equations when measuring a parabola, which is a U-shaped curve that can be graphed on an XY axis with the details that a quadratic equation provides us.

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

How to Work on a Quadratic Equation Utilizing the Quadratic Formula

Even though quadratic equations might seem greatly intricate when starting, they can be divided into few easy steps utilizing an easy formula. The formula for solving quadratic equations includes setting the equal terms and using fundamental algebraic functions like multiplication and division to achieve 2 results.

After all operations have been carried out, we can solve for the values of the variable. The answer take us single step closer to discover answer to our actual question.

Steps to Solving a Quadratic Equation Using the Quadratic Formula

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

ax2 + bx + c=0

Ahead of figuring out 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 both sides of the equation, sum all similar terms on one side, so the left-hand side of the equation equals 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, generally utilizing the perfect square method. If it isn’t possible, put the terms in the quadratic formula, which will be your best buddy for working out quadratic equations. The quadratic formula seems like this:


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

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

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

Example 1

2x2 + 4x - x2 = 5

Now, let’s piece down this equation. First, clarify and place it in the conventional form.

x2 + 4x - 5 = 0

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




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



We figure out the second-degree equation to obtain:



Next, let’s simplify the square root to get two linear equations and figure out:

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

x = 1 x = -5

Now, you have your result! You can revise 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

This is it! You've worked out your first quadratic equation utilizing the quadratic formula! Kudos!

Example 2

Let's try one more example.

3x2 + 13x = 10

First, place it in the standard form so it equals 0.

3x2 + 13x - 10 = 0

To solve this, we will substitute in the values like this:

a = 3

b = 13

c = -10

figure out x utilizing the quadratic formula!



Let’s clarify this as much as workable by figuring it out exactly like we performed in the previous example. Work out all simple equations step by step.



You can figure 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 result! You can review your work 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 this is it! You will work out quadratic equations like nobody’s business with little patience and practice!

Granted this synopsis of quadratic equations and their basic formula, students can now go head on against this difficult topic with confidence. By beginning with this simple explanation, children acquire a firm foundation ahead of moving on to more complex theories down in their studies.

Grade Potential Can Assist You with the Quadratic Equation

If you are fighting to understand these theories, you may need a math tutor to help you. It is better to ask for assistance before you lag behind.

With Grade Potential, you can learn all the handy tricks to ace your subsequent math examination. Grow into a confident quadratic equation solver so you are ready for the ensuing intricate theories in your mathematical studies.