-2/v-6=-3/4v-24+2

Solution for -2/v-6=-3/4v-24+2 equation:

-2/v-6=-3/4v-24+2

We move all terms to the left:

-2/v-6-(-3/4v-24+2)=0


Domain of the equation: v!=0

v∈R



Domain of the equation: 4v-24+2)!=0

We move all terms containing v to the left, all other terms to the right

4v+2)!=24

v∈R


We add all the numbers together, and all the variables

-2/v-(-3/4v-22)-6=0

We get rid of parentheses

-2/v+3/4v+22-6=0

We calculate fractions


(-8v)/4v^2+3v/4v^2+22-6=0

We add all the numbers together, and all the variables

(-8v)/4v^2+3v/4v^2+16=0

We multiply all the terms by the denominator


(-8v)+3v+16*4v^2=0

We add all the numbers together, and all the variables

3v+(-8v)+16*4v^2=0

Wy multiply elements

64v^2+3v+(-8v)=0

We get rid of parentheses

64v^2+3v-8v=0

We add all the numbers together, and all the variables

64v^2-5v=0

a = 64; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·64·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*64}=\frac{0}{128}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*64}=\frac{10}{128}
=5/64
$