-1+2/3m=1/2m-6

Solution for -1+2/3m=1/2m-6 equation:

-1+2/3m=1/2m-6

We move all terms to the left:

-1+2/3m-(1/2m-6)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 2m-6)!=0

m∈R


We get rid of parentheses

2/3m-1/2m+6-1=0

We calculate fractions


4m/6m^2+(-3m)/6m^2+6-1=0

We add all the numbers together, and all the variables

4m/6m^2+(-3m)/6m^2+5=0

We multiply all the terms by the denominator


4m+(-3m)+5*6m^2=0

Wy multiply elements

30m^2+4m+(-3m)=0

We get rid of parentheses

30m^2+4m-3m=0

We add all the numbers together, and all the variables

30m^2+m=0

a = 30; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·30·0
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*30}=\frac{-2}{60}
=-1/30
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*30}=\frac{0}{60}
=0
$