4-2x=8+1/2x

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

4-2x=8+1/2x

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-2x-1/2x-8+4=0

We multiply all the terms by the denominator


-2x*2x-8*2x+4*2x-1=0

Wy multiply elements

-4x^2-16x+8x-1=0

We add all the numbers together, and all the variables

-4x^2-8x-1=0

a = -4; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·(-4)·(-1)
Δ = 48
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{3}}{2*-4}=\frac{8-4\sqrt{3}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{3}}{2*-4}=\frac{8+4\sqrt{3}}{-8}
$