Solving $6200 = (x \times 10000)/(x + 10000)$ I have the following equation: 
$$6200 = (x \times 10000)/(x + 10000)$$
I managed to solve using Microsoft Mathematics. The value is $16,315.7894$. I would like to know how to solve it on paper.
I found that a part of the equation is 
$$6200/2 \times 10,000 \quad\text{or}\quad 6200 / (10000/2) = 31,000,000$$
The result of $16,315.7894 = 31,000,000 / 1900$.
How do I get 1900?
Thank you for helping.
 A: Your given equation
$$
\frac{10^5x}{10^5+x}-6200=0
$$
is equivalent to
$$
38x-620000=0.
$$
So we have
$$
x=\frac{620000}{38}=\frac{2^5\cdot 5^4\cdot 31}{2\cdot 19}=\frac{310000}{19}.
$$
This gives your $19$, or $1900$.
A: $$6200=\frac{10000x}{x+10000}.$$ Multiply $x+10000$ on both sides: $$6200(x+10000)=6200x+62000000=10000x.$$ Subtract $6200x$ on both sides: $$62000000=10000x-6200x=3800x.$$ Divide $3800$ on both sides:$$\frac{62000000}{3800}=x.$$
A: So, you started with $6200 = \dfrac{(x\cdot 10000)}{(x+10000)}$
Assume that $x\neq -10000$ (else you have a division by zero in the above) and multiply both sides by $(x+10000)$ to clear out the fraction on the other side.  That gives us
$$6200\cdot (x+10000) = \dfrac{(x\cdot 10000)}{(x+10000)}\cdot (x+10000)$$
or simplified:
$$6200x + 62000000 = 10000x$$
From here, subtract $6200x$ from each side so that you are left with a variable only on one side of the equation and raw numbers on the other.  You get:
$$62000000 = 3800x$$
Now, just divide both sides by $3800$ and you are done, giving as a final answer
$$x=\frac{62000000}{3800} \approx 16315.789\dots$$
If your question is why we could have written $x$ as $\frac{31000000}{1900}$... that is by dividing top and bottom of the denominator by the same value of $2$.  It is just a fancy way of multiplying by $1$ which of course doesn't change the value of anything.  You can think of it as $$\frac{62000000}{3800}\cdot 1=\frac{62000000}{3800}\cdot\frac{1/2}{1/2}=\frac{62000000/2}{3800/2} = \frac{31000000}{1900}.$$
