1/4v-1=1/v

Solution for 1/4v-1=1/v equation:

1/4v-1=1/v

We move all terms to the left:

1/4v-1-(1/v)=0


Domain of the equation: 4v!=0

v!=0/4

v!=0

v∈R



Domain of the equation: v)!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

1/4v-(+1/v)-1=0

We get rid of parentheses

1/4v-1/v-1=0

We calculate fractions


v/4v^2+(-4v)/4v^2-1=0

We multiply all the terms by the denominator


v+(-4v)-1*4v^2=0

Wy multiply elements

-4v^2+v+(-4v)=0

We get rid of parentheses

-4v^2+v-4v=0

We add all the numbers together, and all the variables

-4v^2-3v=0

a = -4; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-4)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-4}=\frac{0}{-8}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-4}=\frac{6}{-8}
=-3/4
$