1/4v+1=1/2v

Solution for 1/4v+1=1/2v equation:

1/4v+1=1/2v

We move all terms to the left:

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


Domain of the equation: 4v!=0

v!=0/4

v!=0

v∈R



Domain of the equation: 2v)!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/4v-1/2v+1=0

We calculate fractions


2v/8v^2+(-4v)/8v^2+1=0

We multiply all the terms by the denominator


2v+(-4v)+1*8v^2=0

Wy multiply elements

8v^2+2v+(-4v)=0

We get rid of parentheses

8v^2+2v-4v=0

We add all the numbers together, and all the variables

8v^2-2v=0

a = 8; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·8·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*8}=\frac{0}{16}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*8}=\frac{4}{16}
=1/4
$