X+(100/x)-100=0

Solution for X+(100/x)-100=0 equation:

X+(100/X)-100=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+(+100/X)-100=0

We get rid of parentheses

X+100/X-100=0

We multiply all the terms by the denominator


X*X-100*X+100=0

We add all the numbers together, and all the variables

-100X+X*X+100=0

Wy multiply elements

X^2-100X+100=0

a = 1; b = -100; c = +100;
Δ = b2-4ac
Δ = -1002-4·1·100
Δ = 9600
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:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-40\sqrt{6}}{2*1}=\frac{100-40\sqrt{6}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+40\sqrt{6}}{2*1}=\frac{100+40\sqrt{6}}{2}
$