2/3m-4=12+5/6m

Solution for 2/3m-4=12+5/6m equation:

2/3m-4=12+5/6m

We move all terms to the left:

2/3m-4-(12+5/6m)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 6m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

2/3m-(5/6m+12)-4=0

We get rid of parentheses

2/3m-5/6m-12-4=0

We calculate fractions


12m/18m^2+(-15m)/18m^2-12-4=0

We add all the numbers together, and all the variables

12m/18m^2+(-15m)/18m^2-16=0

We multiply all the terms by the denominator


12m+(-15m)-16*18m^2=0

Wy multiply elements

-288m^2+12m+(-15m)=0

We get rid of parentheses

-288m^2+12m-15m=0

We add all the numbers together, and all the variables

-288m^2-3m=0

a = -288; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-288)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-288}=\frac{0}{-576}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-288}=\frac{6}{-576}
=-1/96
$