3/2(2x+4)=1/4(4-8x)

Solution for 3/2(2x+4)=1/4(4-8x) equation:

3/2(2x+4)=1/4(4-8x)

We move all terms to the left:

3/2(2x+4)-(1/4(4-8x))=0


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

x∈R



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

x∈R


We add all the numbers together, and all the variables

3/2(2x+4)-(1/4(-8x+4))=0

We calculate fractions


(12x(-)/(2(2x+4)*4(-8x+4)))+(-2x2/(2(2x+4)*4(-8x+4)))=0


We calculate terms in parentheses: +(12x(-)/(2(2x+4)*4(-8x+4))), so:

12x(-)/(2(2x+4)*4(-8x+4))

We add all the numbers together, and all the variables

12x0/(2(2x+4)*4(-8x+4))

We multiply all the terms by the denominator


12x0

We add all the numbers together, and all the variables

12x

Back to the equation:

+(12x)



We calculate terms in parentheses: +(-2x2/(2(2x+4)*4(-8x+4))), so:

-2x2/(2(2x+4)*4(-8x+4))

We multiply all the terms by the denominator


-2x2

We add all the numbers together, and all the variables

-2x^2

Back to the equation:

+(-2x^2)


We get rid of parentheses

-2x^2+12x=0

a = -2; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-2)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-2}=\frac{-24}{-4}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-2}=\frac{0}{-4}
=0
$