November 24, 2022

Quadratic Equation Formula, Examples

If you going to try to figure out quadratic equations, we are enthusiastic about your journey in mathematics! This is indeed where the most interesting things starts!

The details can appear enormous at start. Despite that, offer yourself a bit of grace and space so there’s no pressure or stress while solving these questions. To be competent 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 heart, a quadratic equation is a math equation that portrays distinct scenarios in which the rate of change is quadratic or proportional to the square of few variable.

Though it seems like an abstract idea, it is simply an algebraic equation stated like a linear equation. It usually has two answers and utilizes intricate roots to work out them, one positive root and one negative, using the quadratic equation. Unraveling both the roots the answer to which will be zero.

Meaning of a Quadratic Equation

Primarily, bear 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 employ this formula to solve for x if we plug these terms into the quadratic formula! (We’ll look at it next.)

All quadratic equations can be scripted like this, that makes working them out simply, comparatively speaking.

Example of a quadratic equation

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

x2 + 5x + 6 = 0

As we can see, there are 2 variables and an independent term, and one of the variables is squared. Therefore, linked to the quadratic equation, we can surely tell this is a quadratic equation.

Usually, 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 gives us.

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

How to Work on a Quadratic Equation Employing the Quadratic Formula

Although quadratic equations may look very complex when starting, they can be broken down into multiple simple steps utilizing a straightforward formula. The formula for working out quadratic equations includes setting the equal terms and applying rudimental algebraic functions like multiplication and division to get two solutions.

Once all functions have been carried out, we can figure out the values of the variable. The results take us single step closer to discover result to our first problem.

Steps to Solving a Quadratic Equation Utilizing the Quadratic Formula

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

ax2 + bx + c=0

Ahead of working on anything, keep in mind to separate the variables on one side of the equation. Here are the three steps to work on a quadratic equation.

Step 1: Write 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 mode of a quadratic equation.

Step 2: Factor the equation if workable

The standard equation you will conclude with should be factored, generally through the perfect square process. If it isn’t possible, put the terms in the quadratic formula, that will be your best friend for solving quadratic equations. The quadratic formula seems similar to this:


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

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

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

Example 1

2x2 + 4x - x2 = 5

Now, let’s fragment down this equation. First, streamline and put it in the conventional form.

x2 + 4x - 5 = 0

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




To figure out quadratic equations, let's plug this into the quadratic formula and solve for “+/-” to involve each square root.



We figure out the second-degree equation to get:



Now, let’s clarify the square root to attain two linear equations and work out:

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

x = 1 x = -5

After that, you have your answers! You can review your work by checking these terms with the original equation.

12 + (4*1) - 5 = 0

1 + 4 - 5 = 0


-52 + (4*-5) - 5 = 0

25 - 20 - 5 = 0

This is it! You've figured out your first quadratic equation utilizing the quadratic formula! Congrats!

Example 2

Let's try one more example.

3x2 + 13x = 10

Initially, put it in the standard form so it equals 0.

3x2 + 13x - 10 = 0

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

a = 3

b = 13

c = -10

Work out x utilizing the quadratic formula!



Let’s clarify this as far as workable by solving it exactly like we executed in the prior example. Figure out all simple equations step by step.



You can work out x by taking the positive and negative 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 that's it! You will solve quadratic equations like a professional with a bit of patience and practice!

Given this summary of quadratic equations and their rudimental formula, children can now take on this challenging topic with assurance. By starting with this easy explanation, children gain a strong understanding before taking on further complicated concepts ahead in their academics.

Grade Potential Can Help You with the Quadratic Equation

If you are fighting to understand these ideas, you may need a mathematics instructor to guide you. It is better to ask for guidance before you fall behind.

With Grade Potential, you can understand all the tips and tricks to ace your subsequent mathematics test. Become a confident quadratic equation solver so you are prepared for the ensuing intricate ideas in your math studies.