1/2m+12=2m

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

1/2m+12=2m

We move all terms to the left:

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


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


-2m*2m+12*2m+1=0

Wy multiply elements

-4m^2+24m+1=0

a = -4; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·(-4)·1
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{37}}{2*-4}=\frac{-24-4\sqrt{37}}{-8}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{37}}{2*-4}=\frac{-24+4\sqrt{37}}{-8}
$