1+1/9x=1/11x

Solution for 1+1/9x=1/11x equation:

1+1/9x=1/11x

We move all terms to the left:

1+1/9x-(1/11x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 11x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/9x-(+1/11x)+1=0

We get rid of parentheses

1/9x-1/11x+1=0

We calculate fractions


11x/99x^2+(-9x)/99x^2+1=0

We multiply all the terms by the denominator


11x+(-9x)+1*99x^2=0

Wy multiply elements

99x^2+11x+(-9x)=0

We get rid of parentheses

99x^2+11x-9x=0

We add all the numbers together, and all the variables

99x^2+2x=0

a = 99; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·99·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*99}=\frac{-4}{198}
=-2/99
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*99}=\frac{0}{198}
=0
$