-5/2v+1/3=-1/3v-6

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

-5/2v+1/3=-1/3v-6

We move all terms to the left:

-5/2v+1/3-(-1/3v-6)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 3v-6)!=0

v∈R


We get rid of parentheses

-5/2v+1/3v+6+1/3=0

We calculate fractions


(-135v)/54v^2+2v/54v^2+2v/54v^2+6=0

We multiply all the terms by the denominator


(-135v)+2v+2v+6*54v^2=0

We add all the numbers together, and all the variables

4v+(-135v)+6*54v^2=0

Wy multiply elements

324v^2+4v+(-135v)=0

We get rid of parentheses

324v^2+4v-135v=0

We add all the numbers together, and all the variables

324v^2-131v=0

a = 324; b = -131; c = 0;
Δ = b2-4ac
Δ = -1312-4·324·0
Δ = 17161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17161}=131$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-131)-131}{2*324}=\frac{0}{648}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-131)+131}{2*324}=\frac{262}{648}
=131/324
$