x/2x-1=3x

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

x/2x-1=3x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

x-3x*2x-1*2x=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-6x^2-1x=0

a = -6; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-6)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-6}=\frac{2}{-12}
=-1/6
$