(3+4x)/(12x)=1/(2x)

Solution for (3+4x)/(12x)=1/(2x) equation:

(3+4x)/(12x)=1/(2x)

We move all terms to the left:

(3+4x)/(12x)-(1/(2x))=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(4x+3)/12x-(+1/2x)=0

We get rid of parentheses

(4x+3)/12x-1/2x=0

We calculate fractions


(8x^2+6x)/24x^2+(-12x)/24x^2=0

We multiply all the terms by the denominator


(8x^2+6x)+(-12x)=0

We get rid of parentheses

8x^2+6x-12x=0

We add all the numbers together, and all the variables

8x^2-6x=0

a = 8; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·8·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*8}=\frac{12}{16}
=3/4
$