1/6v+1=1/4v-1

Solution for 1/6v+1=1/4v-1 equation:

1/6v+1=1/4v-1

We move all terms to the left:

1/6v+1-(1/4v-1)=0


Domain of the equation: 6v!=0

v!=0/6

v!=0

v∈R



Domain of the equation: 4v-1)!=0

v∈R


We get rid of parentheses

1/6v-1/4v+1+1=0

We calculate fractions


4v/24v^2+(-6v)/24v^2+1+1=0

We add all the numbers together, and all the variables

4v/24v^2+(-6v)/24v^2+2=0

We multiply all the terms by the denominator


4v+(-6v)+2*24v^2=0

Wy multiply elements

48v^2+4v+(-6v)=0

We get rid of parentheses

48v^2+4v-6v=0

We add all the numbers together, and all the variables

48v^2-2v=0

a = 48; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·48·0
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*48}=\frac{0}{96}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*48}=\frac{4}{96}
=1/24
$