1/3m+7=1/2m+3

Solution for 1/3m+7=1/2m+3 equation:

1/3m+7=1/2m+3

We move all terms to the left:

1/3m+7-(1/2m+3)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 2m+3)!=0

m∈R


We get rid of parentheses

1/3m-1/2m-3+7=0

We calculate fractions


2m/6m^2+(-3m)/6m^2-3+7=0

We add all the numbers together, and all the variables

2m/6m^2+(-3m)/6m^2+4=0

We multiply all the terms by the denominator


2m+(-3m)+4*6m^2=0

Wy multiply elements

24m^2+2m+(-3m)=0

We get rid of parentheses

24m^2+2m-3m=0

We add all the numbers together, and all the variables

24m^2-1m=0

a = 24; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·24·0
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*24}=\frac{0}{48}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*24}=\frac{2}{48}
=1/24
$