1/100x+1=1/10x

Solution for 1/100x+1=1/10x equation:

1/100x+1=1/10x

We move all terms to the left:

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


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R



Domain of the equation: 10x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/100x-1/10x+1=0

We calculate fractions


10x/1000x^2+(-100x)/1000x^2+1=0

We multiply all the terms by the denominator


10x+(-100x)+1*1000x^2=0

Wy multiply elements

1000x^2+10x+(-100x)=0

We get rid of parentheses

1000x^2+10x-100x=0

We add all the numbers together, and all the variables

1000x^2-90x=0

a = 1000; b = -90; c = 0;
Δ = b2-4ac
Δ = -902-4·1000·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90}{2*1000}=\frac{0}{2000}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90}{2*1000}=\frac{180}{2000}
=9/100
$