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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

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

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

We get rid of parentheses

1/2x-1/2x+1x+3+8=0

We multiply all the terms by the denominator


1x*2x+3*2x+8*2x+1-1=0

We add all the numbers together, and all the variables

1x*2x+3*2x+8*2x=0

Wy multiply elements

2x^2+6x+16x=0

We add all the numbers together, and all the variables

2x^2+22x=0

a = 2; b = 22; c = 0;
Δ = b2-4ac
Δ = 222-4·2·0
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-22}{2*2}=\frac{-44}{4}
=-11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+22}{2*2}=\frac{0}{4}
=0
$