1/2m+3(1/2m+2)=1/2m+4

Solution for 1/2m+3(1/2m+2)=1/2m+4 equation:

1/2m+3(1/2m+2)=1/2m+4

We move all terms to the left:

1/2m+3(1/2m+2)-(1/2m+4)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 2m+2)!=0

m∈R



Domain of the equation: 2m+4)!=0

m∈R


We multiply parentheses

1/2m+3m-(1/2m+4)+6=0

We get rid of parentheses

1/2m+3m-1/2m-4+6=0

We multiply all the terms by the denominator


3m*2m-4*2m+6*2m+1-1=0

We add all the numbers together, and all the variables

3m*2m-4*2m+6*2m=0

Wy multiply elements

6m^2-8m+12m=0

We add all the numbers together, and all the variables

6m^2+4m=0

a = 6; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·6·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*6}=\frac{-8}{12}
=-2/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*6}=\frac{0}{12}
=0
$