1/2(2m+6)=1/4(8-8m)

Solution for 1/2(2m+6)=1/4(8-8m) equation:

1/2(2m+6)=1/4(8-8m)

We move all terms to the left:

1/2(2m+6)-(1/4(8-8m))=0


Domain of the equation: 2(2m+6)!=0

m∈R



Domain of the equation: 4(8-8m))!=0

m∈R


We add all the numbers together, and all the variables

1/2(2m+6)-(1/4(-8m+8))=0

We calculate fractions


(4m(-)/(2(2m+6)*4(-8m+8)))+(-2m2/(2(2m+6)*4(-8m+8)))=0


We calculate terms in parentheses: +(4m(-)/(2(2m+6)*4(-8m+8))), so:

4m(-)/(2(2m+6)*4(-8m+8))

We add all the numbers together, and all the variables

4m0/(2(2m+6)*4(-8m+8))

We multiply all the terms by the denominator


4m0

We add all the numbers together, and all the variables

4m

Back to the equation:

+(4m)



We calculate terms in parentheses: +(-2m2/(2(2m+6)*4(-8m+8))), so:

-2m2/(2(2m+6)*4(-8m+8))

We multiply all the terms by the denominator


-2m2

We add all the numbers together, and all the variables

-2m^2

Back to the equation:

+(-2m^2)


We get rid of parentheses

-2m^2+4m=0

a = -2; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-2)·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*-2}=\frac{-8}{-4}
=+2
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-2}=\frac{0}{-4}
=0
$