X=10000+10000/x

Solution for X=10000+10000/x equation:

X=10000+10000/X

We move all terms to the left:

X-(10000+10000/X)=0


Domain of the equation: X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(10000/X+10000)=0

We get rid of parentheses

X-10000/X-10000=0

We multiply all the terms by the denominator


X*X-10000*X-10000=0

We add all the numbers together, and all the variables

-10000X+X*X-10000=0

Wy multiply elements

X^2-10000X-10000=0

a = 1; b = -10000; c = -10000;
Δ = b2-4ac
Δ = -100002-4·1·(-10000)
Δ = 100040000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{100040000}=\sqrt{40000*2501}=\sqrt{40000}*\sqrt{2501}=200\sqrt{2501}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10000)-200\sqrt{2501}}{2*1}=\frac{10000-200\sqrt{2501}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10000)+200\sqrt{2501}}{2*1}=\frac{10000+200\sqrt{2501}}{2}
$