2/3r-24=1/6r-6

Solution for 2/3r-24=1/6r-6 equation:

2/3r-24=1/6r-6

We move all terms to the left:

2/3r-24-(1/6r-6)=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R



Domain of the equation: 6r-6)!=0

r∈R


We get rid of parentheses

2/3r-1/6r+6-24=0

We calculate fractions


12r/18r^2+(-3r)/18r^2+6-24=0

We add all the numbers together, and all the variables

12r/18r^2+(-3r)/18r^2-18=0

We multiply all the terms by the denominator


12r+(-3r)-18*18r^2=0

Wy multiply elements

-324r^2+12r+(-3r)=0

We get rid of parentheses

-324r^2+12r-3r=0

We add all the numbers together, and all the variables

-324r^2+9r=0

a = -324; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-324)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-324}=\frac{-18}{-648}
=1/36
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-324}=\frac{0}{-648}
=0
$