1/2m=1/3m+12

Solution for 1/2m=1/3m+12 equation:

1/2m=1/3m+12

We move all terms to the left:

1/2m-(1/3m+12)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 3m+12)!=0

m∈R


We get rid of parentheses

1/2m-1/3m-12=0

We calculate fractions


3m/6m^2+(-2m)/6m^2-12=0

We multiply all the terms by the denominator


3m+(-2m)-12*6m^2=0

Wy multiply elements

-72m^2+3m+(-2m)=0

We get rid of parentheses

-72m^2+3m-2m=0

We add all the numbers together, and all the variables

-72m^2+m=0

a = -72; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-72)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-72}=\frac{-2}{-144}
=1/72
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-72}=\frac{0}{-144}
=0
$