1/2m=12-m

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

1/2m=12-m

We move all terms to the left:

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

We get rid of parentheses

1/2m+1m-12=0

We multiply all the terms by the denominator


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

Wy multiply elements

2m^2-24m+1=0

a = 2; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·2·1
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{142}}{2*2}=\frac{24-2\sqrt{142}}{4}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{142}}{2*2}=\frac{24+2\sqrt{142}}{4}
$