1/2m-1=1/4m+13

Solution for 1/2m-1=1/4m+13 equation:

1/2m-1=1/4m+13

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



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

m∈R


We get rid of parentheses

1/2m-1/4m-13-1=0

We calculate fractions


4m/8m^2+(-2m)/8m^2-13-1=0

We add all the numbers together, and all the variables

4m/8m^2+(-2m)/8m^2-14=0

We multiply all the terms by the denominator


4m+(-2m)-14*8m^2=0

Wy multiply elements

-112m^2+4m+(-2m)=0

We get rid of parentheses

-112m^2+4m-2m=0

We add all the numbers together, and all the variables

-112m^2+2m=0

a = -112; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-112)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-112}=\frac{-4}{-224}
=1/56
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-112}=\frac{0}{-224}
=0
$