What is the solution to a quadratic equation?

Answer 1

There are 2 (main) ways you can find the solution to a quadratic equation:

1. Factorisation: If you take, for example, the equation (x-3)(x-2) = 0. Either (x-3) or (x-2) must equal 0 for the equation to be true: you then have x-3 = 0 (i.e. x = 3) and x-2 = 0 (i.e. x = 2). These are your solutions to the equation. If you have an equation in the form (say) x2+x-12 = 0, you can find that this is equivalent to (x-3)(x+4) = 0, so x = 3 or x = -4.
2. The magic formula: If the equation won't factorise, or you can't see how it would, there is a formula you can use to give you both values of x: for any equation ax2+bx+c = 0, x = (-b±√(b2-4ac))/2a. The two values of x come from the ±: one uses a plus and the other a minus.