1/3r-36=1/2r+6

Solution for 1/3r-36=1/2r+6 equation:

1/3r-36=1/2r+6

We move all terms to the left:

1/3r-36-(1/2r+6)=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R



Domain of the equation: 2r+6)!=0

r∈R


We get rid of parentheses

1/3r-1/2r-6-36=0

We calculate fractions


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

We add all the numbers together, and all the variables

2r/6r^2+(-3r)/6r^2-42=0

We multiply all the terms by the denominator


2r+(-3r)-42*6r^2=0

Wy multiply elements

-252r^2+2r+(-3r)=0

We get rid of parentheses

-252r^2+2r-3r=0

We add all the numbers together, and all the variables

-252r^2-1r=0

a = -252; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-252)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-252}=\frac{0}{-504}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-252}=\frac{2}{-504}
=-1/252
$