1/2m+6=2/3m-10

Solution for 1/2m+6=2/3m-10 equation:

1/2m+6=2/3m-10

We move all terms to the left:

1/2m+6-(2/3m-10)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 3m-10)!=0

m∈R


We get rid of parentheses

1/2m-2/3m+10+6=0

We calculate fractions


3m/6m^2+(-4m)/6m^2+10+6=0

We add all the numbers together, and all the variables

3m/6m^2+(-4m)/6m^2+16=0

We multiply all the terms by the denominator


3m+(-4m)+16*6m^2=0

Wy multiply elements

96m^2+3m+(-4m)=0

We get rid of parentheses

96m^2+3m-4m=0

We add all the numbers together, and all the variables

96m^2-1m=0

a = 96; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·96·0
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*96}=\frac{0}{192}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*96}=\frac{2}{192}
=1/96
$