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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

Fractions to decimals

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2+5x+(-1x)=0

We get rid of parentheses

5x^2+5x-1x=0

We add all the numbers together, and all the variables

5x^2+4x=0

a = 5; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·5·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*5}=\frac{-8}{10}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*5}=\frac{0}{10}
=0
$