1/x-1=4/5x

Solution for 1/x-1=4/5x equation:

1/x-1=4/5x

We move all terms to the left:

1/x-1-(4/5x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/x-(+4/5x)-1=0

We get rid of parentheses

1/x-4/5x-1=0

We calculate fractions


5x/5x^2+(-4x)/5x^2-1=0

We multiply all the terms by the denominator


5x+(-4x)-1*5x^2=0

Wy multiply elements

-5x^2+5x+(-4x)=0

We get rid of parentheses

-5x^2+5x-4x=0

We add all the numbers together, and all the variables

-5x^2+x=0

a = -5; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-5)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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