$$n * x * cos(\frac{\pi}2 * \frac{x}{x+b}) + c = y$$
How would I get X on one side of the equation instead of y? Normally I work the equation forwards knowing X. The other variables are constants.
for example: $$0.000025 * 1000 * cos(\frac{\pi}2 * \frac{1000}{1000+7000}) + 0.30 = y$$ $$y = 0.32452$$
What id like to know is given y how do i solve for x? $$0.000025 * x * cos(\frac{\pi}2 * \frac{x}{x+7000}) + 0.30 = 0.32452$$ $$x = ?$$ where x > 0
When the equation contains at the same time polynomial and trigonometric functions, there is no explicit solution for the root(s). This is already the case for the equation $x=\cos(x)$.
Then, you need to consider numerical methods and probably one of the simplest will be Newton method which, starting from a "reasonable" guess $x_0$, will update it according to $$x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$$ Let us play with $$f(x)=0.000025\, x\, \cos(\frac{\pi}2 \, \frac{x}{x+7000}) + 0.30 - 0.34567$$ in order to change from the initial problem (you already know the answer).
If you plot the function over a large range (say from $x=0$ to $x=5000$), you would "see" that there is a root close to $x=2000$. So, let us use $x_0=2000$ and $$f'(x)=0.000025 \cos \left(\frac{\pi x}{2 (x+7000)}\right)-0.000025 x \left(\frac{\pi }{2 (x+7000)}-\frac{\pi x}{2 (x+7000)^2}\right) \sin \left(\frac{\pi x}{2 (x+7000)}\right)$$ and start applying Newton method; this will generate the following iterates $$x_1=1937.90383948004$$ $$x_2=1938.14506264438$$ $$x_3=1938.14506627915$$ which is the solution for fifteen significant figures.