# Solving quadratic equations easily using the quadratic formula (with a calculator)

If you are asked to solve a quadratic equation then you need to use the quadratic formula.

x = [-b ± √{b² - 4ac}]/2a

Quadratic equations which look like ax² + bx + c = 0 can be solved using the quadratic formula shown above. In these worked questions shown below, you will be rounding off your answer either to 1 decimal place or to 2 decimal places.

3x² -2x -7 = 0

Round your solutions to 1 decimal place.

To begin with write down the values of a, b and c.

a = (3), b = (-2) and c = (-7).

Notice that all the numbers have had a bracket put around them. This will eliminate any errors when you type them in on your calculator. Also make sure you have a new scientific calculator that allows you to enter fractions.

Next, substitute these numbers into the quadratic formula:

x = [-b ± √{b² - 4ac}]/2a

x = [-(-2) ± √{(-2)² - 4(3)(-7)}]/2(3)

Now type this exactly into your calculator to get the first solution (change ± to + first of all)

x = [-(-2) + √{(-2)² - 4(3)(-7)}]/2(3)

x = 1.9 to 1 decimal place.

Then get the next solution by changing the ± sign to a -.

x = [-(-2) - √{(-2)² - 4(3)(-7)}]/2(3)

x= -1.2 to 1 decimal place.

So your two solution are x = 1.9 and x = -1.2. These are the places where the quadratic crosses the x axis and are called the roots.

2x² -x -9 = 0

Round your solutions to 2 decimal places.

To begin with write down the values of a, b and c.

a = (2), b = (-1) and c = (-9).

Notice that the number before x is -1.

Next, substitute these numbers into the quadratic formula:

x = [-b ± √{b² - 4ac}]/2a

x = [-(-1) ± √{(-1)² - 4(2)(-9)}]/2(2)

Now type this exactly into your calculator to get the first solution (change ± to + first of all)

x = [-(-1) + √{(-1)² - 4(2)(-9)}]/2(2)

x = 2.39 to 2 decimal places.

Then get the next solution by changing the ± sign to a - sign.

x = [-(-1) + √{(-1)² - 4(2)(-9)}]/2(2)

x= -1.89 to 2 decimal places.

So your two solutions are x = 2.39 and x = -1.89. These are the places where the quadratic equation crosses the x axis and are called the roots.

## More by this Author

Fletcher Tomalty 5 years ago

There's a free online quadratic formula calculator http://quadratic-formula-calculator.com/ that does all this automatically, you don't even need to use a calculator for it.

AEvans 6 years ago from SomeWhere Out There

I enjoyed this lesson on how to solve quadratic equations by using a calculator it is always nice to learn something new! Thumbs up ! :)

0 of 8192 characters used

Mark (catman3000)59 Followers
257 Articles