The Quadratic Formula

This is a clever formula that you can use on a quadratic equation that will almost always solve it.  It seems a bit complicated at first, but is very easy to use once you get used to it.  It runs as follows:

If you have a quadratic equation in the general form:

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Then to find the solutions, use the values of a, b and c in the following formula:


To help you understand it, let’s use it on the first quadratic equation we saw:


For this equation, a = 1, b = 3 and c = 2.  So:


And how we got our answers previously is revealed!  Note how a ‘±’ sign means that there are actually two solutions, one for when it is a ‘+’, and one for when it is a ‘–‘.  Also note how ‘nice’ the solutions are – they don’t have any decimal or fraction parts.  This is not always the case. 

Sometimes you get a negative number underneath the square root sign in the formula.  If this happens, then you can’t solve the quadratic equation – the quadratic equation has no real solutions.  (There are ‘imaginary’ solutions, but you don’t need to know how to get them – just say there is no solution).