12(1/3r+2)=12(1/3r-5)

Solution for 12(1/3r+2)=12(1/3r-5) equation:

12(1/3r+2)=12(1/3r-5)

We move all terms to the left:

12(1/3r+2)-(12(1/3r-5))=0


Domain of the equation: 3r+2)!=0

r∈R



Domain of the equation: 3r-5))!=0

r∈R


We multiply parentheses

12r-(12(1/3r-5))+24=0

We multiply all the terms by the denominator


12r*3r+24*3r-5))-(12(1-5))=0

We add all the numbers together, and all the variables

12r*3r+24*3r-5))-(12(-4))=0

We add all the numbers together, and all the variables

12r*3r+24*3r=0

Wy multiply elements

36r^2+72r=0

a = 36; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·36·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*36}=\frac{-144}{72}
=-2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*36}=\frac{0}{72}
=0
$