1/3m-1=1/4m+13

Solution for 1/3m-1=1/4m+13 equation:

1/3m-1=1/4m+13

We move all terms to the left:

1/3m-1-(1/4m+13)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 4m+13)!=0

m∈R


We get rid of parentheses

1/3m-1/4m-13-1=0

We calculate fractions


4m/12m^2+(-3m)/12m^2-13-1=0

We add all the numbers together, and all the variables

4m/12m^2+(-3m)/12m^2-14=0

We multiply all the terms by the denominator


4m+(-3m)-14*12m^2=0

Wy multiply elements

-168m^2+4m+(-3m)=0

We get rid of parentheses

-168m^2+4m-3m=0

We add all the numbers together, and all the variables

-168m^2+m=0

a = -168; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-168)·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*-168}=\frac{-2}{-336}
=1/168
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-168}=\frac{0}{-336}
=0
$