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e.g. x^2 - (15/2)x = 0. I know I'd usually have to go through the whole factorisation/formula process and get more than one answer for x, but if I know that x is positive am I able to simply divide it by x to get x - 15/2 = 0?

The reason I ask is because this is what I do in my projectile motion questions. Whenever I get a question in which the vertical displacement is 0 (e.g. ball being kicked up then falling back to ground) I end up with the equation 0 = ut + 1/2 at^2 (from the equation of motion s = ut + 1/2 at^2). I always divide this by t and get the right answer, but is this what I'm meant to be doing?

Any help would be greatly appreciated,

David