3/2v+7/v=1

Solution for 3/2v+7/v=1 equation:

3/2v+7/v=1

We move all terms to the left:

3/2v+7/v-(1)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: v!=0

v∈R


We calculate fractions


3v/2v^2+14v/2v^2-1=0

We multiply all the terms by the denominator


3v+14v-1*2v^2=0

We add all the numbers together, and all the variables

17v-1*2v^2=0

Wy multiply elements

-2v^2+17v=0

a = -2; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-2)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-2}=\frac{-34}{-4}
=8+1/2
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-2}=\frac{0}{-4}
=0
$