# Re-arranging a complex equation

I need to re-arrange the following equation (see link JPG below please, sorry I'm not familiar with how to write an equation on here and as I'm a newbie it won't let me post images) to solve for $d$:

$$L = 4\pi C_x d^2.$$

Thank you.

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Try reading the FAQ before posting (always a good idea in any online community): meta.math.stackexchange.com/questions/107/… –  Josh Guffin Dec 2 '10 at 21:22
I'm confused by the image you linked to. I don't really understand how this is a differential equation? Perhaps you could use the following link: codecogs.com/latex/eqneditor.php to produce the equation in latex. You need to take whatever code the box generates and enclose it in dollar signs for it to show up properly. –  WWright Dec 2 '10 at 21:26
As was pointed out in your other question, "make d the subject" will be more understood if you say "solve for d" –  Josh Guffin Dec 2 '10 at 21:26
Sorry, yes I meant 'solve for d'. Just trying to get the hang of writing the equation in latex. –  Dennis Henry Dec 2 '10 at 21:30
@Dennis Henry: Divide. Take square roots. Get rid of the absolute value. –  Arturo Magidin Dec 2 '10 at 21:41

## 1 Answer

As Arturo said

$$L=4 \pi C_x d^2$$

$$\implies d^2 = \frac{L}{4 \pi C_x}$$

$$\implies d= \pm\sqrt{\frac{L}{4 \pi C_x}}$$

Your equation looks like it is physical, so the negative square root may not be relevant

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