(x+3)/3x=x/12

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

(x+3)/3x=x/12

We move all terms to the left:

(x+3)/3x-(x/12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

(x+3)/3x-(+x/12)=0

We get rid of parentheses

(x+3)/3x-x/12=0

We calculate fractions


(-3x^2)/36x+(12x+36)/36x=0

We multiply all the terms by the denominator


(-3x^2)+(12x+36)=0

We get rid of parentheses

-3x^2+12x+36=0

a = -3; b = 12; c = +36;
Δ = b2-4ac
Δ = 122-4·(-3)·36
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-24}{2*-3}=\frac{-36}{-6}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+24}{2*-3}=\frac{12}{-6}
=-2
$