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In the equation "you = mgh", divide both sides of the equation by mg, or you/mg = mgh/mg. The answer then is h = you/mg.
An example of a wrong function equation is f(x) = sqrt(x) for all non-negative x.
Basically, if you check the dimensions of an equation and get different dimensions on the left and on the right, the equation is definitely wrong. If you get the same dimensions, it MAY be right.
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A dimensional check in an equation can provide a quick check about the possible correctness of the equation. For example, if you are supposed to calculate a speed, the dimensions of the result MUST be of the form [distance] / [time] (or something that you can simplify to distance/time). If it doesn't, the formula is wrong. If it does, it MIGHT be correct.