9/7v+2/v=1

Solution for 9/7v+2/v=1 equation:

9/7v+2/v=1

We move all terms to the left:

9/7v+2/v-(1)=0


Domain of the equation: 7v!=0

v!=0/7

v!=0

v∈R



Domain of the equation: v!=0

v∈R


We calculate fractions


9v/7v^2+14v/7v^2-1=0

We multiply all the terms by the denominator


9v+14v-1*7v^2=0

We add all the numbers together, and all the variables

23v-1*7v^2=0

Wy multiply elements

-7v^2+23v=0

a = -7; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-7)·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*-7}=\frac{-46}{-14}
=3+2/7
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-7}=\frac{0}{-14}
=0
$