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

Solution for (-1/x)+(2/6x)=2 equation:

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

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

We get rid of parentheses

-12x^2+2x-6x=0

We add all the numbers together, and all the variables

-12x^2-4x=0

a = -12; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-12)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-12}=\frac{8}{-24}
=-1/3
$