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

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

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

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



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

m∈R


We get rid of parentheses

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

We calculate fractions


27m/54m^2+(-4m)/54m^2+4m/54m^2-2=0

We multiply all the terms by the denominator


27m+(-4m)+4m-2*54m^2=0

We add all the numbers together, and all the variables

31m+(-4m)-2*54m^2=0

Wy multiply elements

-108m^2+31m+(-4m)=0

We get rid of parentheses

-108m^2+31m-4m=0

We add all the numbers together, and all the variables

-108m^2+27m=0

a = -108; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-108)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-108}=\frac{-54}{-216}
=1/4
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-108}=\frac{0}{-216}
=0
$