16-1/2(2x)=8-1/2(x)

Solution for 16-1/2(2x)=8-1/2(x) equation:

16-1/2(2x)=8-1/2(x)

We move all terms to the left:

16-1/2(2x)-(8-1/2(x))=0


Domain of the equation: 22x!=0

x!=0/22

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/22x-(-1/2x+8)+16=0

We get rid of parentheses

-1/22x+1/2x-8+16=0

We calculate fractions


(-2x)/44x^2+22x/44x^2-8+16=0

We add all the numbers together, and all the variables

(-2x)/44x^2+22x/44x^2+8=0

We multiply all the terms by the denominator


(-2x)+22x+8*44x^2=0

We add all the numbers together, and all the variables

22x+(-2x)+8*44x^2=0

Wy multiply elements

352x^2+22x+(-2x)=0

We get rid of parentheses

352x^2+22x-2x=0

We add all the numbers together, and all the variables

352x^2+20x=0

a = 352; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·352·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*352}=\frac{-40}{704}
=-5/88
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*352}=\frac{0}{704}
=0
$