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 get rid of parentheses

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-1=0

a = 6; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·6·(-1)
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*6}=\frac{-2-2\sqrt{7}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*6}=\frac{-2+2\sqrt{7}}{12}
$