-7/3v+1/5=-7/5v-7

Solution for -7/3v+1/5=-7/5v-7 equation:

-7/3v+1/5=-7/5v-7

We move all terms to the left:

-7/3v+1/5-(-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+1/5=0

We calculate fractions


(-875v)/375v^2+21v/375v^2+3v/375v^2+7=0

We multiply all the terms by the denominator


(-875v)+21v+3v+7*375v^2=0

We add all the numbers together, and all the variables

24v+(-875v)+7*375v^2=0

Wy multiply elements

2625v^2+24v+(-875v)=0

We get rid of parentheses

2625v^2+24v-875v=0

We add all the numbers together, and all the variables

2625v^2-851v=0

a = 2625; b = -851; c = 0;
Δ = b2-4ac
Δ = -8512-4·2625·0
Δ = 724201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{724201}=851$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-851)-851}{2*2625}=\frac{0}{5250}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-851)+851}{2*2625}=\frac{1702}{5250}
=851/2625
$