3/x-1/2x-1=2

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

3/x-1/2x-1=2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We add all the numbers together, and all the variables

6x/2x^2+(-1x)/2x^2-3=0

We multiply all the terms by the denominator


6x+(-1x)-3*2x^2=0

Wy multiply elements

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

We get rid of parentheses

-6x^2+6x-1x=0

We add all the numbers together, and all the variables

-6x^2+5x=0

a = -6; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-6)·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*-6}=\frac{-10}{-12}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-6}=\frac{0}{-12}
=0
$