3m+6=1/2m

Solution for 3m+6=1/2m equation:

3m+6=1/2m

We move all terms to the left:

3m+6-(1/2m)=0


Domain of the equation: 2m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

3m-(+1/2m)+6=0

We get rid of parentheses

3m-1/2m+6=0

We multiply all the terms by the denominator


3m*2m+6*2m-1=0

Wy multiply elements

6m^2+12m-1=0

a = 6; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·6·(-1)
Δ = 168
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:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{42}}{2*6}=\frac{-12-2\sqrt{42}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{42}}{2*6}=\frac{-12+2\sqrt{42}}{12}
$