2v+7=3/v=

Solution for 2v+7=3/v= equation:

2v+7=3/v=

We move all terms to the left:

2v+7-(3/v)=0


Domain of the equation: v)!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

2v-(+3/v)+7=0

We get rid of parentheses

2v-3/v+7=0

We multiply all the terms by the denominator


2v*v+7*v-3=0

We add all the numbers together, and all the variables

7v+2v*v-3=0

Wy multiply elements

2v^2+7v-3=0

a = 2; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·2·(-3)
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{73}}{2*2}=\frac{-7-\sqrt{73}}{4}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{73}}{2*2}=\frac{-7+\sqrt{73}}{4}
$