20/3x-5=5/x-2

Solution for 20/3x-5=5/x-2 equation:

20/3x-5=5/x-2

We move all terms to the left:

20/3x-5-(5/x-2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

20/3x-5/x+2-5=0

We calculate fractions


20x/3x^2+(-15x)/3x^2+2-5=0

We add all the numbers together, and all the variables

20x/3x^2+(-15x)/3x^2-3=0

We multiply all the terms by the denominator


20x+(-15x)-3*3x^2=0

Wy multiply elements

-9x^2+20x+(-15x)=0

We get rid of parentheses

-9x^2+20x-15x=0

We add all the numbers together, and all the variables

-9x^2+5x=0

a = -9; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-9)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-9}=\frac{-10}{-18}
=5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-9}=\frac{0}{-18}
=0
$