2/3m+2=-3+3/2m

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

2/3m+2=-3+3/2m

We move all terms to the left:

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


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 2m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


4m/6m^2+(-9m)/6m^2+3+2=0

We add all the numbers together, and all the variables

4m/6m^2+(-9m)/6m^2+5=0

We multiply all the terms by the denominator


4m+(-9m)+5*6m^2=0

Wy multiply elements

30m^2+4m+(-9m)=0

We get rid of parentheses

30m^2+4m-9m=0

We add all the numbers together, and all the variables

30m^2-5m=0

a = 30; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·30·0
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*30}=\frac{0}{60}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*30}=\frac{10}{60}
=1/6
$