1/8x-1=1/2x-2

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

1/8x-1=1/2x-2

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


2x+(-8x)+1*16x^2=0

Wy multiply elements

16x^2+2x+(-8x)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

16x^2-6x=0

a = 16; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·16·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*16}=\frac{12}{32}
=3/8
$