12/2m-1=12/m+4

Solution for 12/2m-1=12/m+4 equation:

12/2m-1=12/m+4

We move all terms to the left:

12/2m-1-(12/m+4)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: m+4)!=0

m∈R


We get rid of parentheses

12/2m-12/m-4-1=0

We calculate fractions


12m/2m^2+(-24m)/2m^2-4-1=0

We add all the numbers together, and all the variables

12m/2m^2+(-24m)/2m^2-5=0

We multiply all the terms by the denominator


12m+(-24m)-5*2m^2=0

Wy multiply elements

-10m^2+12m+(-24m)=0

We get rid of parentheses

-10m^2+12m-24m=0

We add all the numbers together, and all the variables

-10m^2-12m=0

a = -10; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-10)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-10}=\frac{0}{-20}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-10}=\frac{24}{-20}
=-1+1/5
$