2/3m=3/2m-4

Solution for 2/3m=3/2m-4 equation:

2/3m=3/2m-4

We move all terms to the left:

2/3m-(3/2m-4)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 2m-4)!=0

m∈R


We get rid of parentheses

2/3m-3/2m+4=0

We calculate fractions


4m/6m^2+(-9m)/6m^2+4=0

We multiply all the terms by the denominator


4m+(-9m)+4*6m^2=0

Wy multiply elements

24m^2+4m+(-9m)=0

We get rid of parentheses

24m^2+4m-9m=0

We add all the numbers together, and all the variables

24m^2-5m=0

a = 24; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·24·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*24}=\frac{0}{48}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*24}=\frac{10}{48}
=5/24
$