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For a software project, I need to calculate some things. on of the formulas looks like:

26280 = 2 * SQRT((149,598,000,000 - x) / 1.4) + x / 10,217,588,910,387,300,000 

My colegue says you can't solve the above equation (you won't be able to find x) I quite convinced you should be able to find x, the problem is, I don't know how :(

I came as far as rewriting the above into:

((26280 - x) / 20,435,177,820,774,600,000)^2 = (149,598,000,000 - x) / 1.4 

but now I'm stuck.

Could anyone explain to me how to move on, in order to find x?

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    The two equations you have written are not equivalent. The two answers below address the second one, but it's not the same as the first. Because the numbers are so large, the solutions to both equations are approximately the same.2012-04-05

2 Answers 2

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First, it's useful to write the expression in the standard quadratic form. For ease of reading/writing, I'm going to set $A = 20,435,177,820,744,600,00$ and $B = 149,598,000,000$.

$ \begin{align*} \left(\frac{26280 - x}{A}\right)^2 &= \frac{B - x}{1.4}\\ \frac{(26280 - x)^2}{A^2} &= \frac{B}{1.4} - \frac{x}{1.4}\\ \frac{26280^2 - 52560x - x^2}{A^2} &= \frac{5}{7}B - \frac{5}{7}x\\ \frac{26280^2}{A^2} - \frac{52560x}{A^2} - \frac{x^2}{A^2} &= \frac{5}{7}B - \frac{5}{7}x\\ 0 &= \frac{x^2}{A^2} + \left(\frac{52560}{A^2} - \frac{5}{7}\right)x + \frac{5}{7}B - \frac{26280^2}{A^2}. \end{align*} $

You can finish this up with the quadratic formula.

EDIT: Alternatively, there is WolframAlpha.

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    yeah, the resulting number is about a distance, so we will ignore the negative solution.2012-04-05
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As Austin Mohr said it's a quadratic equation. You must only expand. Their solutions are: -298283208976198672964919958167422500864 and 149598000000.