1/2-1/m+2=1/2m+4

Solution for 1/2-1/m+2=1/2m+4 equation:

1/2-1/m+2=1/2m+4

We move all terms to the left:

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


Domain of the equation: m!=0

m∈R



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

m∈R


We get rid of parentheses

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

We calculate fractions


(-8m)/8m^2+(-m)/8m^2+m/8m^2-4+2=0

We add all the numbers together, and all the variables

(-8m)/8m^2+(-1m)/8m^2+m/8m^2-4+2=0

We add all the numbers together, and all the variables

(-8m)/8m^2+(-1m)/8m^2+m/8m^2-2=0

We multiply all the terms by the denominator


(-8m)+(-1m)+m-2*8m^2=0

We add all the numbers together, and all the variables

m+(-8m)+(-1m)-2*8m^2=0

Wy multiply elements

-16m^2+m+(-8m)+(-1m)=0

We get rid of parentheses

-16m^2+m-8m-1m=0

We add all the numbers together, and all the variables

-16m^2-8m=0

a = -16; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-16)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-16}=\frac{0}{-32}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-16}=\frac{16}{-32}
=-1/2
$