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

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

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

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 3m-3)!=0

m∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

3m/6m^2+4m/6m^2+1=0

We multiply all the terms by the denominator


3m+4m+1*6m^2=0

We add all the numbers together, and all the variables

7m+1*6m^2=0

Wy multiply elements

6m^2+7m=0

a = 6; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·6·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*6}=\frac{-14}{12}
=-1+1/6
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*6}=\frac{0}{12}
=0
$