7/3v-4/5=-7/5v-7

Solution for 7/3v-4/5=-7/5v-7 equation:

7/3v-4/5=-7/5v-7

We move all terms to the left:

7/3v-4/5-(-7/5v-7)=0


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R



Domain of the equation: 5v-7)!=0

v∈R


We get rid of parentheses

7/3v+7/5v+7-4/5=0

We calculate fractions


875v/375v^2+21v/375v^2+(-12v)/375v^2+7=0

We multiply all the terms by the denominator


875v+21v+(-12v)+7*375v^2=0

We add all the numbers together, and all the variables

896v+(-12v)+7*375v^2=0

Wy multiply elements

2625v^2+896v+(-12v)=0

We get rid of parentheses

2625v^2+896v-12v=0

We add all the numbers together, and all the variables

2625v^2+884v=0

a = 2625; b = 884; c = 0;
Δ = b2-4ac
Δ = 8842-4·2625·0
Δ = 781456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{781456}=884$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(884)-884}{2*2625}=\frac{-1768}{5250}
=-884/2625
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(884)+884}{2*2625}=\frac{0}{5250}
=0
$