I've gotten stuck trying to solve the equation below for y. It's a tricky one for me as my algebra skills are basic at best.

I have managed to get somewhere but the answer that comes out of the final equation is about 17% error from starting equation when I plug some numbers into it.

Have I missed something or is there a better way?

Start with 2 equations:

- $\displaystyle y^2=r^2+x^2$ and
- $\displaystyle y=\frac{wx}{r}-d$

Need to substitute equation 2 into 1 and solve for y. Then resubstitute and solve for x. (Only r, w, and d are known).

I got to this:

3. $\displaystyle y=\frac{w}{r}(\sqrt{y^2-r^2})-d$

But this leaves me with $\displaystyle y^2$

on the RHS under the square root. From here is were I am unsure.

I managed to get to this:

4. $\displaystyle y=\{\frac{1}{1-(\frac{r}{w})^2}[(\frac{dr}{w})^2+r^2]\}^0^.^5$

This got rid of y and x from RHS however, when I input some values to check if it works I get a different value for y between equations 3 and 4.

Values I used are:

r=3

w=12

d=11

x=4

y=5

(had to use a number for y in eq. 3 to check it works)

Same numbers in eq.4 y = 4.341?

Have I gone about this the right way? what am I missing?

Thanks.