2m-1=27/2m-1

Solution for 2m-1=27/2m-1 equation:

2m-1=27/2m-1

We move all terms to the left:

2m-1-(27/2m-1)=0


Domain of the equation: 2m-1)!=0

m∈R


We get rid of parentheses

2m-27/2m+1-1=0

We multiply all the terms by the denominator


2m*2m+1*2m-1*2m-27=0

Wy multiply elements

4m^2+2m-2m-27=0

We add all the numbers together, and all the variables

4m^2-27=0

a = 4; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·4·(-27)
Δ = 432
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*4}=\frac{0-12\sqrt{3}}{8}
=-\frac{12\sqrt{3}}{8}
=-\frac{3\sqrt{3}}{2}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*4}=\frac{0+12\sqrt{3}}{8}
=\frac{12\sqrt{3}}{8}
=\frac{3\sqrt{3}}{2}
$