1+1/11x=1/13x

Solution for 1+1/11x=1/13x equation:

1+1/11x=1/13x

We move all terms to the left:

1+1/11x-(1/13x)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R



Domain of the equation: 13x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/11x-(+1/13x)+1=0

We get rid of parentheses

1/11x-1/13x+1=0

We calculate fractions


13x/143x^2+(-11x)/143x^2+1=0

We multiply all the terms by the denominator


13x+(-11x)+1*143x^2=0

Wy multiply elements

143x^2+13x+(-11x)=0

We get rid of parentheses

143x^2+13x-11x=0

We add all the numbers together, and all the variables

143x^2+2x=0

a = 143; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·143·0
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*143}=\frac{-4}{286}
=-2/143
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*143}=\frac{0}{286}
=0
$