November 24, 2022

Quadratic Equation Formula, Examples

If this is your first try to work on quadratic equations, we are thrilled about your adventure in mathematics! This is really where the fun begins!

The details can appear overwhelming at first. Despite that, offer yourself some grace and room so there’s no rush or strain while solving these problems. To master quadratic equations like a pro, you will require 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 arithmetic formula that describes different scenarios in which the rate of deviation is quadratic or relative to the square of few variable.

However it may look like an abstract idea, it is just an algebraic equation stated like a linear equation. It usually has two solutions and uses complicated roots to solve them, one positive root and one negative, through the quadratic equation. Working out 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 use this formula to solve for x if we plug these numbers into the quadratic formula! (We’ll look at it next.)

Any quadratic equations can be scripted like this, which makes solving them straightforward, relatively speaking.

Example of a quadratic equation

Let’s contrast the ensuing 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. Therefore, compared to the quadratic equation, we can confidently say this is a quadratic equation.

Usually, you can find these kinds of equations when scaling a parabola, which is a U-shaped curve that can be plotted on an XY axis with the information that a quadratic equation gives us.

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

How to Figure out a Quadratic Equation Employing the Quadratic Formula

Although quadratic equations might look very complex when starting, they can be broken down into multiple simple steps employing a simple formula. The formula for figuring out quadratic equations consists of creating the equal terms and applying rudimental algebraic operations like multiplication and division to obtain two results.

After all operations have been performed, we can work out the values of the variable. The results take us one step nearer to discover answer to our actual question.

Steps to Figuring out a Quadratic Equation Employing the Quadratic Formula

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

ax2 + bx + c=0

Prior to figuring out anything, bear in mind to separate the variables on one side of the equation. Here are the 3 steps to solve a quadratic equation.

Step 1: Write the equation in standard mode.

If there are terms on either side of the equation, sum all alike terms on one side, so the left-hand side of the equation equals zero, just like the conventional mode of a quadratic equation.

Step 2: Factor the equation if possible

The standard equation you will end up with should be factored, usually utilizing the perfect square method. If it isn’t possible, replace the terms in the quadratic formula, that will be your best friend for working out quadratic equations. The quadratic formula looks something like this:


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

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

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

Example 1

2x2 + 4x - x2 = 5

At the moment, let’s fragment down this equation. First, streamline and put it in the standard form.

x2 + 4x - 5 = 0

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




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



We work on the second-degree equation to obtain:



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

Next, you have your result! You can review your solution 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 using the quadratic formula! Kudos!

Example 2

Let's check out another example.

3x2 + 13x = 10

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

3x2 + 13x - 10 = 0

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

a = 3

b = 13

c = -10

Solve for x employing the quadratic formula!



Let’s streamline this as far as possible by working it out just like we performed in the last example. Solve 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 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 solve quadratic equations like nobody’s business with little patience and practice!

Granted this overview of quadratic equations and their rudimental formula, students can now go head on against this challenging topic with assurance. By opening with this easy explanation, children acquire a solid grasp prior undertaking further intricate ideas later in their studies.

Grade Potential Can Help You with the Quadratic Equation

If you are battling to understand these concepts, you might need a math teacher to assist you. It is better to ask for assistance before you lag behind.

With Grade Potential, you can study all the tips and tricks to ace your subsequent mathematics examination. Grow into a confident quadratic equation solver so you are ready for the following big theories in your mathematical studies.