Hi, first of all ALL quadratic equations have solutions. Lots more to say,but we'll keep it simple.These are an extremely important family of functions lots of reasons ; they even describe the shape of your tv satellite dish!

The ones you'll be seeing will either factorise nicely,or the formula will always get you there.That is

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)A quick way too see if it's going to factorise nicely is to look at the expression inside the square root sign,that is \(b^2-4ac\)

If \(b^2-4ac\)is a positive square number ie 16, 25, 81 etc it will always factorise nicely. But if you are having difficulty factorising (it's just lots of practise!) the formual will always work too.

{If \(b^2-4ac\)is negative,you will not at this stage in your maths career be able to solve the quadratic, but you will not be asked to solve one of these. If you were to look at a graph of a quadratic where b^2 -4ac is negative,you would see that the curve never touches the x -axis. Sometimes,you might be asked to find the maximum or minmum value of one of these curves,using a technique called Completing the Square.}

Plenty of people on here I'm sure will be happy to help you, just do lots of examples and you will soon get the technique of factorising.