(1/3v-18)-2=3/v-6

Solution for (1/3v-18)-2=3/v-6 equation:

(1/3v-18)-2=3/v-6

We move all terms to the left:

(1/3v-18)-2-(3/v-6)=0


Domain of the equation: 3v-18)!=0

v∈R



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

v∈R


We get rid of parentheses

1/3v-3/v-18+6-2=0

We calculate fractions


v/3v^2+(-9v)/3v^2-18+6-2=0

We add all the numbers together, and all the variables

v/3v^2+(-9v)/3v^2-14=0

We multiply all the terms by the denominator


v+(-9v)-14*3v^2=0

Wy multiply elements

-42v^2+v+(-9v)=0

We get rid of parentheses

-42v^2+v-9v=0

We add all the numbers together, and all the variables

-42v^2-8v=0

a = -42; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-42)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-42}=\frac{0}{-84}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-42}=\frac{16}{-84}
=-4/21
$