1/6r-(1/3r)=-2

Solution for 1/6r-(1/3r)=-2 equation:

1/6r-(1/3r)=-2

We move all terms to the left:

1/6r-(1/3r)-(-2)=0


Domain of the equation: 6r!=0

r!=0/6

r!=0

r∈R



Domain of the equation: 3r)!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

1/6r-(+1/3r)-(-2)=0

We add all the numbers together, and all the variables

1/6r-(+1/3r)+2=0

We get rid of parentheses

1/6r-1/3r+2=0

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

36r^2+3r+(-6r)=0

We get rid of parentheses

36r^2+3r-6r=0

We add all the numbers together, and all the variables

36r^2-3r=0

a = 36; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·36·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*36}=\frac{0}{72}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*36}=\frac{6}{72}
=1/12
$