1/6x-6=1/18x+6

Solution for 1/6x-6=1/18x+6 equation:

1/6x-6=1/18x+6

We move all terms to the left:

1/6x-6-(1/18x+6)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 18x+6)!=0

x∈R


We get rid of parentheses

1/6x-1/18x-6-6=0

We calculate fractions


18x/108x^2+(-6x)/108x^2-6-6=0

We add all the numbers together, and all the variables

18x/108x^2+(-6x)/108x^2-12=0

We multiply all the terms by the denominator


18x+(-6x)-12*108x^2=0

Wy multiply elements

-1296x^2+18x+(-6x)=0

We get rid of parentheses

-1296x^2+18x-6x=0

We add all the numbers together, and all the variables

-1296x^2+12x=0

a = -1296; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-1296)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-1296}=\frac{-24}{-2592}
=1/108
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-1296}=\frac{0}{-2592}
=0
$