# Thread: help re-arranging a complex formula

1. ## help re-arranging a complex formula

Hi,
I'm having some trouble rearranging the formula below in terms of t, i'm sure its much easier than I think but if would be great if i could be pointed in the right direction. Its been a while since I've had to do something like this so im quite rusty!

I've got several equations like this which i wil need to arrange and im wondering if it can be done in Mathcad, which I have but im not familer with?

any help much appreciated

mark

2. Originally Posted by markanswrth
Hi,
I'm having some trouble rearranging the formula below in terms of t, i'm sure its much easier than I think but if would be great if i could be pointed in the right direction. Its been a while since I've had to do something like this so im quite rusty!

I've got several equations like this which i wil need to arrange and im wondering if it can be done in Mathcad, which I have but im not familer with?

any help much appreciated

mark
First of all you can cancellate $t^4$ with the $t$ under $s$ as there's a multiplication, and then we get:

$F=\frac{4E}{1-\mu^2}\cdot \frac{t^3}{K_1\cdot D_e^2}\cdot s\left[\left(\frac{h_0-s}{t}\right)\left(\frac{2h_0-s}{2t}\right)+1\right]$ $=\frac{4E}{1-\mu^2}\cdot \frac{t^3}{K_1\cdot D_e^2}\cdot s\left[\frac{2h_0^2-3h_0s+s^2}{2t^2}+1\right]=$

$\frac{4E}{1-\mu^2}\cdot \frac{t^3}{K_1\cdot D_e^2}\cdot s\left(\frac{2h_0^2-3h_0s+s^2+2t^2}{2t^2}\right)$

Now cancellate $t^3$ with the $t^2$ inside the parentheses, getting

$\frac{4E}{1-\mu^2}\cdot \frac{t}{K_1\cdot D_e^2}\cdot s\left(\frac{2h_0^2-3h_0s+s^2+2t^2}{2}\right)=$ $\frac{4E}{1-\mu^2}\cdot \frac{t}{K_1\cdot D_e^2}\cdot \frac{s}{2}\left(2h_0^2-3h_0s+s^2+2t^2\right)$[/tex]

leaving now all what's attached to $t$ in the right side and passing to the left one all the rest we get a cubic in $t$ which, still, is pretty nasty, but at least closer to what you, perhaps, want.

Tonio