-7/3v-7/4=1/4v-1

Solution for -7/3v-7/4=1/4v-1 equation:

-7/3v-7/4=1/4v-1

We move all terms to the left:

-7/3v-7/4-(1/4v-1)=0


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R



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

v∈R


We get rid of parentheses

-7/3v-1/4v+1-7/4=0

We calculate fractions


(-448v)/192v^2+(-3v)/192v^2+(-21v)/192v^2+1=0

We multiply all the terms by the denominator


(-448v)+(-3v)+(-21v)+1*192v^2=0

Wy multiply elements

192v^2+(-448v)+(-3v)+(-21v)=0

We get rid of parentheses

192v^2-448v-3v-21v=0

We add all the numbers together, and all the variables

192v^2-472v=0

a = 192; b = -472; c = 0;
Δ = b2-4ac
Δ = -4722-4·192·0
Δ = 222784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{222784}=472$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-472)-472}{2*192}=\frac{0}{384}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-472)+472}{2*192}=\frac{944}{384}
=2+11/24
$