<s>[INST] how to find x in the following formula 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?
 [/INST] 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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