1/6r+2=1/9r+6

Solution for 1/6r+2=1/9r+6 equation:

1/6r+2=1/9r+6

We move all terms to the left:

1/6r+2-(1/9r+6)=0


Domain of the equation: 6r!=0

r!=0/6

r!=0

r∈R



Domain of the equation: 9r+6)!=0

r∈R


We get rid of parentheses

1/6r-1/9r-6+2=0

We calculate fractions


9r/54r^2+(-6r)/54r^2-6+2=0

We add all the numbers together, and all the variables

9r/54r^2+(-6r)/54r^2-4=0

We multiply all the terms by the denominator


9r+(-6r)-4*54r^2=0

Wy multiply elements

-216r^2+9r+(-6r)=0

We get rid of parentheses

-216r^2+9r-6r=0

We add all the numbers together, and all the variables

-216r^2+3r=0

a = -216; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-216)·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*-216}=\frac{-6}{-432}
=1/72
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-216}=\frac{0}{-432}
=0
$