23/8+7/6v=21/4v-2

Solution for 23/8+7/6v=21/4v-2 equation:

23/8+7/6v=21/4v-2

We move all terms to the left:

23/8+7/6v-(21/4v-2)=0


Domain of the equation: 6v!=0

v!=0/6

v!=0

v∈R



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

v∈R


We get rid of parentheses

7/6v-21/4v+2+23/8=0

We calculate fractions


2208v^2/1536v^2+1792v/1536v^2+(-8064v)/1536v^2+2=0

We multiply all the terms by the denominator


2208v^2+1792v+(-8064v)+2*1536v^2=0

Wy multiply elements

2208v^2+3072v^2+1792v+(-8064v)=0

We get rid of parentheses

2208v^2+3072v^2+1792v-8064v=0

We add all the numbers together, and all the variables

5280v^2-6272v=0

a = 5280; b = -6272; c = 0;
Δ = b2-4ac
Δ = -62722-4·5280·0
Δ = 39337984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39337984}=6272$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6272)-6272}{2*5280}=\frac{0}{10560}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6272)+6272}{2*5280}=\frac{12544}{10560}
=1+31/165
$