In these lessons, we will learn how to use the Quadratic Formula to solve quadratic equations. This method is usually used when it is too difficult to solve the quadratic equation by factoring and other methods or when the solutions are not integers.

**Related Pages**

Solving Quadratic Equations by Completing the Square

Factoring Out Common Factors (GCF)

More Lessons for Grade 8

Math Worksheets

Factoring Quadratic Equations using Perfect Square Trinomial (Square of a Sum) or Square of a Difference) or Difference of Two Squares.

Factoring Quadratic Equations where the coefficient of x^{2} is 1.

Factoring Quadratic Equations by Completing the Square

Factoring Quadratic Equations where the coefficient of x^{2} is greater than 1

**What is the Quadratic Formula?**

The following diagrams gives the Quadratic Formula and how to use it to solve quadratic equations. Scroll down the page for more examples and solutions of the quadratic formula.

Given the quadratic equation ax^{2} + bx + c, we can find the values of x by using the
Quadratic Formula:

Let us consider an example.

**Example:**

Find the values of x for the equation: 4x^{2} + 26x + 12 = 0

**Solution:**

Step 1: From the equation:

a = 4, b = 26 and c = 12

Step 2: Plug into the formula. The ± sign means there are two values, one with + and the other with –.

Answer:

Quadratic equations have at most two real solutions, as in the example above.

However, some quadratic equations have only one real solution. If the quadratic equation has only one solution, the expression under the square root symbol in the quadratic formula is equal to 0, and so adding or subtracting 0 yields the same result.

Other quadratic equations have no real solutions; for example, In this case, the expression under the square root symbol is negative, so the entire expression is not a real number.

Have a look at the following videos for more examples on the use of quadratic formula to solve equations:

**Using the Quadratic Formula to find solutions to quadratic equations**

**Example:**

Solve 9x^{2} - 9x + 2 = 0

**Example:**

Solve 3x^{2} + √11x + 2 = 0

**Example:**

Solve 3x^{2} + 5x = 7

**Solving quadratic equations using the quadratic formula.**

**Examples:**

Solve x^{2} - 5x - 6 = 0

Solve 2x^{2} - 4x - 7 = 0

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