5/3-1/3v-3=1/v-1

Solution for 5/3-1/3v-3=1/v-1 equation:

5/3-1/3v-3=1/v-1

We move all terms to the left:

5/3-1/3v-3-(1/v-1)=0


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R



Domain of the equation: v-1)!=0

v∈R


We get rid of parentheses

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

We calculate fractions


(-v)/27v^2+(-27v)/27v^2+5v/27v^2+1-3=0

We add all the numbers together, and all the variables

(-1v)/27v^2+(-27v)/27v^2+5v/27v^2+1-3=0

We add all the numbers together, and all the variables

(-1v)/27v^2+(-27v)/27v^2+5v/27v^2-2=0

We multiply all the terms by the denominator


(-1v)+(-27v)+5v-2*27v^2=0

We add all the numbers together, and all the variables

5v+(-1v)+(-27v)-2*27v^2=0

Wy multiply elements

-54v^2+5v+(-1v)+(-27v)=0

We get rid of parentheses

-54v^2+5v-1v-27v=0

We add all the numbers together, and all the variables

-54v^2-23v=0

a = -54; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-54)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*-54}=\frac{0}{-108}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-54}=\frac{46}{-108}
=-23/54
$