(-2/3r)=5/6r-36

Solution for (-2/3r)=5/6r-36 equation:

(-2/3r)=5/6r-36

We move all terms to the left:

(-2/3r)-(5/6r-36)=0


Domain of the equation: 3r)!=0

r!=0/1

r!=0

r∈R



Domain of the equation: 6r-36)!=0

r∈R


We get rid of parentheses

-2/3r-5/6r+36=0

We calculate fractions


(-12r)/18r^2+(-15r)/18r^2+36=0

We multiply all the terms by the denominator


(-12r)+(-15r)+36*18r^2=0

Wy multiply elements

648r^2+(-12r)+(-15r)=0

We get rid of parentheses

648r^2-12r-15r=0

We add all the numbers together, and all the variables

648r^2-27r=0

a = 648; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·648·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*648}=\frac{0}{1296}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*648}=\frac{54}{1296}
=1/24
$