(1)/(6)x-(1)/(3)x=1

Solution for (1)/(6)x-(1)/(3)x=1 equation:

(1)/(6)x-(1)/(3)x=1

We move all terms to the left:

(1)/(6)x-(1)/(3)x-(1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


3x/18x^2+(-6x)/18x^2-1=0

We multiply all the terms by the denominator


3x+(-6x)-1*18x^2=0

Wy multiply elements

-18x^2+3x+(-6x)=0

We get rid of parentheses

-18x^2+3x-6x=0

We add all the numbers together, and all the variables

-18x^2-3x=0

a = -18; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-18)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-18}=\frac{0}{-36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-18}=\frac{6}{-36}
=-1/6
$