1/7v+5/v=1

Solution for 1/7v+5/v=1 equation:

1/7v+5/v=1

We move all terms to the left:

1/7v+5/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


v/7v^2+35v/7v^2-1=0

We multiply all the terms by the denominator


v+35v-1*7v^2=0

We add all the numbers together, and all the variables

36v-1*7v^2=0

Wy multiply elements

-7v^2+36v=0

a = -7; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·(-7)·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*-7}=\frac{-72}{-14}
=5+1/7
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*-7}=\frac{0}{-14}
=0
$