2x-1=2/x

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

2x-1=2/x

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x-2/x-1=0

We multiply all the terms by the denominator


2x*x-1*x-2=0

We add all the numbers together, and all the variables

-1x+2x*x-2=0

Wy multiply elements

2x^2-1x-2=0

a = 2; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·2·(-2)
Δ = 17
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{17}}{2*2}=\frac{1-\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{17}}{2*2}=\frac{1+\sqrt{17}}{4}
$