1/3r-5/6r-2=1

Solution for 1/3r-5/6r-2=1 equation:

1/3r-5/6r-2=1

We move all terms to the left:

1/3r-5/6r-2-(1)=0


Domain of the equation: 3r!=0

r!=0/3

r!=0

r∈R



Domain of the equation: 6r!=0

r!=0/6

r!=0

r∈R


We add all the numbers together, and all the variables

1/3r-5/6r-3=0

We calculate fractions


6r/18r^2+(-15r)/18r^2-3=0

We multiply all the terms by the denominator


6r+(-15r)-3*18r^2=0

Wy multiply elements

-54r^2+6r+(-15r)=0

We get rid of parentheses

-54r^2+6r-15r=0

We add all the numbers together, and all the variables

-54r^2-9r=0

a = -54; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-54)·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*-54}=\frac{0}{-108}
=0
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-54}=\frac{18}{-108}
=-1/6
$