November 24, 2022

Quadratic Equation Formula, Examples

If you going to try to solve quadratic equations, we are enthusiastic about your journey in mathematics! This is really where the amusing part begins!

The information can appear overwhelming at start. However, give yourself a bit of grace and space so there’s no rush or strain when working through these problems. To be competent at quadratic equations like an expert, you will need understanding, patience, and a sense of humor.

Now, let’s start learning!

What Is the Quadratic Equation?

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

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

Meaning of a Quadratic Equation

Foremost, 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 conventional form is:

ax2 + bx + c

Where “a,” “b,” and “c” are variables. We can use this equation to solve for x if we put these variables into the quadratic formula! (We’ll go through it 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 following 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. Consequently, linked to the quadratic equation, we can confidently tell this is a quadratic equation.

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

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

How to Work on a Quadratic Equation Utilizing the Quadratic Formula

Although quadratic equations may appear greatly complex initially, they can be broken down into multiple easy steps using a straightforward formula. The formula for working out quadratic equations includes setting the equal terms and applying fundamental algebraic functions like multiplication and division to achieve 2 solutions.

After all functions have been executed, we can work out the numbers of the variable. The results take us single step nearer to work out the solutions to our first problem.

Steps to Figuring out a Quadratic Equation Using the Quadratic Formula

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

ax2 + bx + c=0

Prior to figuring out anything, remember to detach the variables on one side of the equation. Here are the 3 steps to solve a quadratic equation.

Step 1: Note the equation in conventional mode.

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

Step 2: Factor the equation if feasible

The standard equation you will wind up with must be factored, generally utilizing the perfect square method. If it isn’t feasible, replace the terms in the quadratic formula, that will be your best friend for figuring out quadratic equations. The quadratic formula appears something like this:


Every terms coincide to the equivalent terms in a standard form of a quadratic equation. You’ll be using this a great deal, so it is smart move to memorize it.

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

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

Example 1

2x2 + 4x - x2 = 5

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

x2 + 4x - 5 = 0

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




To solve 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 clarify the square root to get two linear equations and solve:

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

x = 1 x = -5

Now, you have your solution! You can check your work by checking 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! Congrats!

Example 2

Let's check out one more example.

3x2 + 13x = 10

Initially, place it in the standard form so it equals zero.

3x2 + 13x - 10 = 0

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

a = 3

b = 13

c = -10

figure out x utilizing the quadratic formula!



Let’s streamline this as much as workable by solving it just like we performed in the prior example. Solve all easy equations step by step.



You can work out x by considering the negative and positive square roots.

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

x=46 x=-306

x=23 x=-5

Now, you have your result! You can revise your work 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 work out quadratic equations like a pro with some practice and patience!

Given this overview of quadratic equations and their rudimental formula, children can now tackle this difficult topic with assurance. By starting with this simple definitions, kids gain a firm understanding ahead of undertaking further complicated theories later in their studies.

Grade Potential Can Assist You with the Quadratic Equation

If you are fighting to get a grasp these concepts, you may need a mathematics tutor to guide you. It is better to ask for help before you fall behind.

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