(3v-5/v)=2

Solution for (3v-5/v)=2 equation:

(3v-5/v)=2

We move all terms to the left:

(3v-5/v)-(2)=0


Domain of the equation: v)!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3v-5/v-2=0

We multiply all the terms by the denominator


3v*v-2*v-5=0

We add all the numbers together, and all the variables

-2v+3v*v-5=0

Wy multiply elements

3v^2-2v-5=0

a = 3; b = -2; c = -5;
Δ = b2-4ac
Δ = -22-4·3·(-5)
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{-(-2)-8}{2*3}=\frac{-6}{6}
=-1
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+8}{2*3}=\frac{10}{6}
=1+2/3
$