Since the picture doesn't show the error message, it would be helpful if you told us what it is. Even better, post the worksheet (in the edit dialog, click on "Use advanced editor" at the top right).
I need the euqations because I need to develop an equation.... If use values then I am not going to be able to develop the equation. here is a code. Any help will be appreciated!
Why do you need the equation? Like lturek, I don't think you will find a closed form solution. I also tried the Maple symbolic engine used in earlier versions of Mathcad, and it does not give anything useful either.
At the end you demand Mathcad to solve an equation like R*u^5+u^3-1=0 symbolically, which it can't do - like many other math packages, including On-line Wolfram Alpha. (u=x^0.5 and R=ratio^2.5).
I don't think that you will be able to get a closed solution to this equation.
There is no closed formula to solve an algebraic equation of fifth order.
But as Alan pointed out Mathcad can provide a numerical solution for any given ratio.
And you will get a pair (x,y) where both are in the range (0,1) for any positive ratio Rs/Rt.
I am not sure what you would need a closed expression for, but I guess the best you will be able to achieve is the creation of a lookup table for the values of x with respect to the value of the Ratio Rs/Rt which can be used by another (embedded?) program to provide the values.
It's not clear to me what defines the distance OA. The distance OB is the distance from the origin to the intersection of the curves y=(Rs/Rt)*x and y^2.5+x^1.5=1, but what is OA?
Today I know that equation is wrong... Looks to me that is been used as an approximation. I am planning on doing it graphically.. and see if I find a pattern that will help find simplify my equation. Yep I agree there is no way this equation can be easily solve the way it is.
