20/3x-7=20/x-1

Solution for 20/3x-7=20/x-1 equation:

20/3x-7=20/x-1

We move all terms to the left:

20/3x-7-(20/x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

x∈R


We get rid of parentheses

20/3x-20/x+1-7=0

We calculate fractions


20x/3x^2+(-60x)/3x^2+1-7=0

We add all the numbers together, and all the variables

20x/3x^2+(-60x)/3x^2-6=0

We multiply all the terms by the denominator


20x+(-60x)-6*3x^2=0

Wy multiply elements

-18x^2+20x+(-60x)=0

We get rid of parentheses

-18x^2+20x-60x=0

We add all the numbers together, and all the variables

-18x^2-40x=0

a = -18; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·(-18)·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*-18}=\frac{0}{-36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*-18}=\frac{80}{-36}
=-2+2/9
$