How to solve for x in this equation

[frankivalli]

How to solve for "x" in this equation

Thanks in advance:

here is my equation:

Area = $\pi$r$^{2}$ - r$^{2}$(arcos((r-x)/r))+(r-x))*$\sqrt{2*r*x-x^{2}}$

 

[Mark44]

Thanks in advance:

here is my equation:

Area = $\pi$r$^{2}$ - r$^{2}$(arcos((r-x)/r))+(r-x))*$\sqrt{2*r*x-x^{2}}$

Is this related to the question you asked in another thread about the height of a liquid in a horizontal, cylindrical tank?

If so, I don't think you can solve the equation above analytically for x. The best you can do is solve it numerically using some approximation technique.

 

[ModusPwnd]

Do you know about transcendental equations? A numerical or graphical solution is probably needed.

http://mathworld.wolfram.com/TranscendentalFunction.html
http://en.wikipedia.org/wiki/Transcendental_equation