3/x-1=8/2x

Solution for 3/x-1=8/2x equation:

3/x-1=8/2x

We move all terms to the left:

3/x-1-(8/2x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/x-(+8/2x)-1=0

We get rid of parentheses

3/x-8/2x-1=0

We calculate fractions


6x/2x^2+(-8x)/2x^2-1=0

We multiply all the terms by the denominator


6x+(-8x)-1*2x^2=0

Wy multiply elements

-2x^2+6x+(-8x)=0

We get rid of parentheses

-2x^2+6x-8x=0

We add all the numbers together, and all the variables

-2x^2-2x=0

a = -2; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-2)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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