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

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

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

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-2x)/12x^2+(-6x)/12x^2-2=0

We multiply all the terms by the denominator


(-2x)+(-6x)-2*12x^2=0

Wy multiply elements

-24x^2+(-2x)+(-6x)=0

We get rid of parentheses

-24x^2-2x-6x=0

We add all the numbers together, and all the variables

-24x^2-8x=0

a = -24; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-24)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-24}=\frac{16}{-48}
=-1/3
$