1/2x-1/8=1/6x

Solution for 1/2x-1/8=1/6x equation:

1/2x-1/8=1/6x

We move all terms to the left:

1/2x-1/8-(1/6x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(+1/6x)-1/8=0

We get rid of parentheses

1/2x-1/6x-1/8=0

We calculate fractions


(-72x^2)/768x^2+384x/768x^2+(-128x)/768x^2=0

We multiply all the terms by the denominator


(-72x^2)+384x+(-128x)=0

We get rid of parentheses

-72x^2+384x-128x=0

We add all the numbers together, and all the variables

-72x^2+256x=0

a = -72; b = 256; c = 0;
Δ = b2-4ac
Δ = 2562-4·(-72)·0
Δ = 65536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{65536}=256$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(256)-256}{2*-72}=\frac{-512}{-144}
=3+5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(256)+256}{2*-72}=\frac{0}{-144}
=0
$