1/4(16-4x)=1/2(2x+16)

Solution for 1/4(16-4x)=1/2(2x+16) equation:

1/4(16-4x)=1/2(2x+16)

We move all terms to the left:

1/4(16-4x)-(1/2(2x+16))=0


Domain of the equation: 4(16-4x)!=0

x∈R



Domain of the equation: 2(2x+16))!=0

x∈R


We add all the numbers together, and all the variables

1/4(-4x+16)-(1/2(2x+16))=0

We calculate fractions


(2x2/(4(-4x+16)*2(2x+16)))+(-4x0/(4(-4x+16)*2(2x+16)))=0


We calculate terms in parentheses: +(2x2/(4(-4x+16)*2(2x+16))), so:

2x2/(4(-4x+16)*2(2x+16))

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 calculate terms in parentheses: +(-4x0/(4(-4x+16)*2(2x+16))), so:

-4x0/(4(-4x+16)*2(2x+16))

We multiply all the terms by the denominator


-4x0

We add all the numbers together, and all the variables

-4x

Back to the equation:

+(-4x)


We get rid of parentheses

2x^2-4x=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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*2}=\frac{8}{4}
=2
$