X+(1/10x)=100

Solution for X+(1/10x)=100 equation:

X+(1/10X)=100

We move all terms to the left:

X+(1/10X)-(100)=0


Domain of the equation: 10X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X+(+1/10X)-100=0

We get rid of parentheses

X+1/10X-100=0

We multiply all the terms by the denominator


X*10X-100*10X+1=0

Wy multiply elements

10X^2-1000X+1=0

a = 10; b = -1000; c = +1;
Δ = b2-4ac
Δ = -10002-4·10·1
Δ = 999960
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:

$\sqrt{\Delta}=\sqrt{999960}=\sqrt{4*249990}=\sqrt{4}*\sqrt{249990}=2\sqrt{249990}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-2\sqrt{249990}}{2*10}=\frac{1000-2\sqrt{249990}}{20}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+2\sqrt{249990}}{2*10}=\frac{1000+2\sqrt{249990}}{20}
$