1/2m=92,m=

Solution for 1/2m=92,m= equation:

1/2m=92.m=

We move all terms to the left:

1/2m-(92.m)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

1/2m-(+92.m)=0

We get rid of parentheses

1/2m-92.m=0

We multiply all the terms by the denominator


-(92.m)*2m+1=0

We add all the numbers together, and all the variables

-(+92.m)*2m+1=0

We multiply parentheses

-184m^2+1=0

a = -184; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-184)·1
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{46}}{2*-184}=\frac{0-4\sqrt{46}}{-368}
=-\frac{4\sqrt{46}}{-368}
=-\frac{\sqrt{46}}{-92}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{46}}{2*-184}=\frac{0+4\sqrt{46}}{-368}
=\frac{4\sqrt{46}}{-368}
=\frac{\sqrt{46}}{-92}
$