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

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

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

We move all terms to the left:

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


Domain of the equation: 6v!=0

v!=0/6

v!=0

v∈R



Domain of the equation: 2v-5)!=0

v∈R


We get rid of parentheses

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

We calculate fractions


24v^2/108v^2+(-18v)/108v^2+270v/108v^2+5=0

We multiply all the terms by the denominator


24v^2+(-18v)+270v+5*108v^2=0

We add all the numbers together, and all the variables

24v^2+270v+(-18v)+5*108v^2=0

Wy multiply elements

24v^2+540v^2+270v+(-18v)=0

We get rid of parentheses

24v^2+540v^2+270v-18v=0

We add all the numbers together, and all the variables

564v^2+252v=0

a = 564; b = 252; c = 0;
Δ = b2-4ac
Δ = 2522-4·564·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-252}{2*564}=\frac{-504}{1128}
=-21/47
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+252}{2*564}=\frac{0}{1128}
=0
$