1/2x-12=1/8x

Solution for 1/2x-12=1/8x equation:

1/2x-12=1/8x

We move all terms to the left:

1/2x-12-(1/8x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(+1/8x)-12=0

We get rid of parentheses

1/2x-1/8x-12=0

We calculate fractions


8x/16x^2+(-2x)/16x^2-12=0

We multiply all the terms by the denominator


8x+(-2x)-12*16x^2=0

Wy multiply elements

-192x^2+8x+(-2x)=0

We get rid of parentheses

-192x^2+8x-2x=0

We add all the numbers together, and all the variables

-192x^2+6x=0

a = -192; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-192)·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*-192}=\frac{-12}{-384}
=1/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-192}=\frac{0}{-384}
=0
$