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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


128x^2/512x^2+256x/512x^2+(-128x)/512x^2+2=0

We multiply all the terms by the denominator


128x^2+256x+(-128x)+2*512x^2=0

Wy multiply elements

128x^2+1024x^2+256x+(-128x)=0

We get rid of parentheses

128x^2+1024x^2+256x-128x=0

We add all the numbers together, and all the variables

1152x^2+128x=0

a = 1152; b = 128; c = 0;
Δ = b2-4ac
Δ = 1282-4·1152·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-128}{2*1152}=\frac{-256}{2304}
=-1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+128}{2*1152}=\frac{0}{2304}
=0
$