3x-1=(1/2x)

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

3x-1=(1/2x)

We move all terms to the left:

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


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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-2x=0

a = 6; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·6·0
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*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*6}=\frac{4}{12}
=1/3
$