1/3v-6=6-1/6v

Solution for 1/3v-6=6-1/6v equation:

1/3v-6=6-1/6v

We move all terms to the left:

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


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R



Domain of the equation: 6v)!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

1/3v-(-1/6v+6)-6=0

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

6v/18v^2+3v/18v^2-12=0

We multiply all the terms by the denominator


6v+3v-12*18v^2=0

We add all the numbers together, and all the variables

9v-12*18v^2=0

Wy multiply elements

-216v^2+9v=0

a = -216; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-216)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-216}=\frac{-18}{-432}
=1/24
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-216}=\frac{0}{-432}
=0
$