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

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

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

We move all terms to the left:

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


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-12m^2)/72m^2+48m/72m^2+(-108m)/72m^2=0

We multiply all the terms by the denominator


(-12m^2)+48m+(-108m)=0

We get rid of parentheses

-12m^2+48m-108m=0

We add all the numbers together, and all the variables

-12m^2-60m=0

a = -12; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·(-12)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*-12}=\frac{0}{-24}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*-12}=\frac{120}{-24}
=-5
$