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

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

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

We move all terms to the left:

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


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



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

m∈R


We get rid of parentheses

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

We calculate fractions


12m/18m^2+(-3m)/18m^2+6+2=0

We add all the numbers together, and all the variables

12m/18m^2+(-3m)/18m^2+8=0

We multiply all the terms by the denominator


12m+(-3m)+8*18m^2=0

Wy multiply elements

144m^2+12m+(-3m)=0

We get rid of parentheses

144m^2+12m-3m=0

We add all the numbers together, and all the variables

144m^2+9m=0

a = 144; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·144·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*144}=\frac{-18}{288}
=-1/16
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*144}=\frac{0}{288}
=0
$