I have an equation, where acceleration is affected by a driving power and air resistance. The acceleration is given by:(adsbygoogle = window.adsbygoogle || []).push({});

a = (2P / m + u^2)^0.5 - (k*p*A*u^2 / 2m) - u

I'm trying to make "u" the subject, which is previous velocity, to find at what velocity does acceleration become 0, the maximum speed. However, this has proven to be very difficult for me, and the closest I have gotten is:

8P / k*m*p = k*p*u^4 + 4*u^3

However, this does not have "u" by itself. I have gotten "u" by itself, but it requires cube rooting or even 4th rooting (I don't know the term) the other side of the equation, and still has "u" in that...

I'm hoping there's a nice easy way of fixing this, but I can't seem to find it. I have tried online calculators, and my ClassPad, but they give very large and complex answers.

Thanks for any help.

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# Solving for a variable, transposing equation

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