November 24, 2022

Quadratic Equation Formula, Examples

If you’re starting to work on quadratic equations, we are enthusiastic regarding your venture in mathematics! This is indeed where the most interesting things starts!

The details can appear too much at start. But, offer yourself a bit of grace and space so there’s no pressure or stress when figuring out these problems. To master quadratic equations like an expert, you will require patience, understanding, and a sense of humor.

Now, let’s start learning!

What Is the Quadratic Equation?

At its core, a quadratic equation is a math formula that states various scenarios in which the rate of change is quadratic or proportional to the square of some variable.

However it seems similar to an abstract idea, it is just an algebraic equation stated like a linear equation. It usually has two results and uses complicated roots to work out them, one positive root and one negative, using the quadratic equation. Unraveling both the roots should equal zero.

Meaning of a Quadratic Equation

Foremost, remember that a quadratic expression is a polynomial equation that comprises of 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 figure out x if we replace these numbers into the quadratic equation! (We’ll get to that later.)

Ever quadratic equations can be written like this, which results in figuring them out simply, comparatively speaking.

Example of a quadratic equation

Let’s compare the following equation to the previous equation:

x2 + 5x + 6 = 0

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

Generally, you can see these types of equations when measuring a parabola, that 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 know what quadratic equations are and what they look like, let’s move forward to figuring them out.

How to Work on a Quadratic Equation Using the Quadratic Formula

Although quadratic equations may look very complex initially, they can be cut down into few easy steps employing an easy formula. The formula for solving quadratic equations consists of setting the equal terms and utilizing basic algebraic operations like multiplication and division to obtain 2 answers.

Once all functions have been performed, we can solve for the values of the variable. The results take us single step nearer to work out the answer to our original question.

Steps to Figuring out a Quadratic Equation Utilizing the Quadratic Formula

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

ax2 + bx + c=0

Before solving anything, remember to isolate the variables on one side of the equation. Here are the three steps to solve a quadratic equation.

Step 1: Write 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 equals zero, just like the standard model of a quadratic equation.

Step 2: Factor the equation if feasible

The standard equation you will conclude with should be factored, ordinarily utilizing the perfect square method. If it isn’t feasible, replace the terms in the quadratic formula, which will be your best buddy for figuring out quadratic equations. The quadratic formula appears something like this:


All the terms correspond to the same terms in a conventional form of a quadratic equation. You’ll be employing this a lot, so it pays to memorize it.

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

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

Example 1

2x2 + 4x - x2 = 5

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

x2 + 4x - 5 = 0

Immediately, let's identify 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 put this into the quadratic formula and find the solution “+/-” to include both square root.



We solve the second-degree equation to achieve:



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

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

x = 1 x = -5

After that, you have your solution! You can check 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 using the quadratic formula! Kudos!

Example 2

Let's check out another example.

3x2 + 13x = 10

First, put it in the standard form so it results in zero.

3x2 + 13x - 10 = 0

To figure out this, we will plug in the numbers like this:

a = 3

b = 13

c = -10

Work out x using the quadratic formula!



Let’s clarify this as far as feasible by working it out just like we executed in the prior example. Solve all simple equations step by step.



You can solve for x by taking the negative and positive square roots.

x=-13+176 x=-13-176

x=46 x=-306

x=23 x=-5

Now, you have your solution! You can check your workings using 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 figure out quadratic equations like nobody’s business with some patience and practice!

With this summary of quadratic equations and their rudimental formula, students can now go head on against this difficult topic with assurance. By opening with this straightforward definitions, kids secure a solid foundation prior moving on to further complicated ideas down in their academics.

Grade Potential Can Help You with the Quadratic Equation

If you are battling to understand these ideas, you might require a mathematics teacher to assist you. It is better to ask for assistance before you fall behind.

With Grade Potential, you can learn all the helpful hints to ace your subsequent mathematics examination. Turn into a confident quadratic equation solver so you are ready for the ensuing big ideas in your math studies.