Solve using the quadratic formula


This lesson shows how to solve using the quadratic formula. To use the quadratic formula, you need to identify a, b, and c in the standard of a quadratic equation


Quadratic Formula is x = (-b ± √(b2 - 4ac))/2a


The standard form is ax2 + bx + c = 0

1) for 6x2 + 8x + 7 = 0 we get a = 6, b = 8, and c = 7

2) for x2 + 8x - 7 = 0 we get a = 1, b = 8, and c = -7

2) for -x2 - 8x + 7 = 0 we get a = -1, b = -8, and c = 7


Example #1:


Solve using the quadratic formula x2 + 8x + 7 = 0

a = 1, b = 8, and c = 7

x = (-b ± √(b2 - 4ac)) / 2a

x = (-8 ± √(82 - 4 × 1 × 7)) / 2 × 1

x = (-8 ± √(64 - 4 × 1 × 7)) / 2

x = (-8 ± √(64 - 4 × 7)) / 2

x = (-8 ± √(64 - 28)) / 2

x = (-8 ± √(36)) / 2

x = (-8 ± 6 ) / 2

x1 = (-8 + 6 ) / 2

x1 = (-2 ) / 2

x1 = -1

x2 = (-8 - 6 ) / 2

x2 = (-14 ) / 2

x2 = -7


Example #2:


Solve using the quadratic formula 4x2 - 11x - 3 = 0

a = 4, b = -11, and c = -3

x = (-b ± √(b2 - 4ac)) / 2a

x = (- -11 ± √(  (-11)2  - 4 × 4 × -3)) / 2 × 4

x = (11 ± √(121 - 4 × 4 × -3)) / 8

x = (11 ± √(121 - 4 × -12)) / 8

x = (11 ± √(121 + 48)) / 8

x = (11 ± √(169)) / 8

x = (11 ± 13 ) / 8

x1 = (11 + 13 ) / 8

x1 = (24 ) / 8

x1 = 3

x2 = (11 - 13 ) / 8

x2 = (-2 ) / 8

x2 = -1/4


Example #3:


Solve using the quadratic formula x2 + x - 2 = 0

a = 1, b = 1, and c = -2

x = (-b ± √(b2 - 4ac)) / 2a

x = (- 1 ± √(  (1)2  - 4 × 1 × -2)) / 2 × 1

x = (-1 ± √(1 - 4 × 1 × -2)) / 2

x = (-1 ± √(1 - 4 × -2)) / 2

x = (-1 ± √(1 + 8)) / 2

x = (-1 ± √(9)) / 2

x = (-1 ± 3 ) / 2

x1 = (-1 + 3 ) / 2

x1 = (2) / 2

x1 = 1

x2 = (-1 - 3 ) / 2

x2 = (-4 ) / 2

x2 = -2




Recent Articles

  1. Proof that There is no Rational Number Whose Square is 2

    Feb 17, 19 12:04 PM

    There is no rational number whose square is 2. An easy to follow proof by contraction.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest


Math quizzes

 Recommended

Scientific Notation Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz

Types of angles quiz


Tough algebra word problems

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Recent Articles

  1. Proof that There is no Rational Number Whose Square is 2

    Feb 17, 19 12:04 PM

    There is no rational number whose square is 2. An easy to follow proof by contraction.

    Read More

K-12 math tests


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.