X-(1/10x)=110

Solution for X-(1/10x)=110 equation:

X-(1/10X)=110

We move all terms to the left:

X-(1/10X)-(110)=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)-110=0

We get rid of parentheses

X-1/10X-110=0

We multiply all the terms by the denominator


X*10X-110*10X-1=0

Wy multiply elements

10X^2-1100X-1=0

a = 10; b = -1100; c = -1;
Δ = b2-4ac
Δ = -11002-4·10·(-1)
Δ = 1210040
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:

$\sqrt{\Delta}=\sqrt{1210040}=\sqrt{676*1790}=\sqrt{676}*\sqrt{1790}=26\sqrt{1790}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1100)-26\sqrt{1790}}{2*10}=\frac{1100-26\sqrt{1790}}{20}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1100)+26\sqrt{1790}}{2*10}=\frac{1100+26\sqrt{1790}}{20}
$