# Thread: Rearranging a Difficult Equation

1. ## Rearranging a Difficult Equation

Hi all,

I've been trying (unsuccessfully!) to rearrange the following equation so that H is the subject:

mgH = [k(H - L)^2] / 2

(Where ^2 means squared.) I also have some test data which shows that if m = 50, g = 9.8, k = 40 and L = 20, H should equal 57.5, or thereabouts.

I'm going to need the equation in a couple of hours and am stressing out, so any help you can offer would be greatly appreciated.

2. Originally Posted by mothonthewall86
Hi all,

I've been trying (unsuccessfully!) to rearrange the following equation so that H is the subject:

mgH = [k(H - L)^2] / 2

(Where ^2 means squared.) I also have some test data which shows that if m = 50, g = 9.8, k = 40 and L = 20, H should equal 57.5, or thereabouts.

I'm going to need the equation in a couple of hours and am stressing out, so any help you can offer would be greatly appreciated.
$mgH = \frac{k}{2}(H^2 - 2HL + L^2)$

$mgH = \frac{k}{2}H^2 - kHL + \frac{k}{2}L^2$

$0 = \frac{k}{2}H^2 - kHL - mgH + \frac{k}{2}L^2$

$0 = \frac{k}{2}H^2 - (kL + mg)H + \frac{k}{2}L^2$

use the quadratic formula ... $H = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$ , where ...

$a = \frac{k}{2}$ , $b = -(kL + mg)$ , $c = \frac{k}{2}L^2$

3. $mgH = \frac{k(H - L)^2}{2}$

Multiply both sides by 2

$2mgH = k(H - L)^2$

Multiply out the brackets

$2mgH = k(H^2 - 2LH + L^2)$ = $2mgH = kH^2 - 2LkH + kL^2$.

You now have a quadratic, rearrange and solve for H.

4. I must be dense for not seeing that. Internet strangers, you are my knights in shining armor!

Thanks so much for your help.