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I have this equation:

v*t-(u*g*t^2)/2 = d

And I'm having trouble solving it for t. Mathematica gave me two results,

t -> (v+-Sqrt[-2 d g u+v^2])/(g u)

Have no idea how it got it. I did manage to get to t = (d+0.5u*g*t)/v or t^2 = (v*t-d)/(0.5u*)

Any help will be appreciated. Thanks!n

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up vote 4 down vote accepted

The equation can be written as $-ugt^2+2vt-2d=0$. The quadratic formula then gives $t=\dfrac{-2v\pm\sqrt{4v^2-4(-ug)(-2d)}}{-2ug}$, which is equivalent to what Mathematica gave you.

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Thanks! Helped me a lot. – Mark Segal Jan 24 '12 at 13:51

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