Algebra rearrangement, solve for x

Question

How do I solve this equation for x?

$$1.43 = \frac{x}{0.99x+5.21\times10^{-5}}$$

I have tried rearranging it, but can't seem to get a positive number.

Answer 1

Let $A = 1.43, B=0.99, C = 5.21 \times 10^{-5}$

The equation is $A = \frac{x}{Bx + C}$

Rearranging,

$ABx + AC = x$

$x(AB-1) = -AC$

$x = \frac{AC}{1-AB}$

which evaluates to approximately $x = -1.792 \times 10^{-4}$, indeed a negative real number.