1/3m+4=5/6m+2

Solution for 1/3m+4=5/6m+2 equation:

1/3m+4=5/6m+2

We move all terms to the left:

1/3m+4-(5/6m+2)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



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

m∈R


We get rid of parentheses

1/3m-5/6m-2+4=0

We calculate fractions


6m/18m^2+(-15m)/18m^2-2+4=0

We add all the numbers together, and all the variables

6m/18m^2+(-15m)/18m^2+2=0

We multiply all the terms by the denominator


6m+(-15m)+2*18m^2=0

Wy multiply elements

36m^2+6m+(-15m)=0

We get rid of parentheses

36m^2+6m-15m=0

We add all the numbers together, and all the variables

36m^2-9m=0

a = 36; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·36·0
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*36}=\frac{0}{72}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*36}=\frac{18}{72}
=1/4
$