-1/9x+5/9=1/5x-1

Solution for -1/9x+5/9=1/5x-1 equation:

-1/9x+5/9=1/5x-1

We move all terms to the left:

-1/9x+5/9-(1/5x-1)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 5x-1)!=0

x∈R


We get rid of parentheses

-1/9x-1/5x+1+5/9=0

We calculate fractions


(-5x)/3645x^2+(-729x)/3645x^2+25x/3645x^2+1=0

We multiply all the terms by the denominator


(-5x)+(-729x)+25x+1*3645x^2=0

We add all the numbers together, and all the variables

25x+(-5x)+(-729x)+1*3645x^2=0

Wy multiply elements

3645x^2+25x+(-5x)+(-729x)=0

We get rid of parentheses

3645x^2+25x-5x-729x=0

We add all the numbers together, and all the variables

3645x^2-709x=0

a = 3645; b = -709; c = 0;
Δ = b2-4ac
Δ = -7092-4·3645·0
Δ = 502681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{502681}=709$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-709)-709}{2*3645}=\frac{0}{7290}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-709)+709}{2*3645}=\frac{1418}{7290}
=709/3645
$