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

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

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

We move all terms to the left:

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


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R



Domain of the equation: 5v-4)!=0

v∈R


We get rid of parentheses

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

We calculate fractions


35v/135v^2+189v/135v^2+(-35v)/135v^2+4=0

We multiply all the terms by the denominator


35v+189v+(-35v)+4*135v^2=0

We add all the numbers together, and all the variables

224v+(-35v)+4*135v^2=0

Wy multiply elements

540v^2+224v+(-35v)=0

We get rid of parentheses

540v^2+224v-35v=0

We add all the numbers together, and all the variables

540v^2+189v=0

a = 540; b = 189; c = 0;
Δ = b2-4ac
Δ = 1892-4·540·0
Δ = 35721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{35721}=189$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(189)-189}{2*540}=\frac{-378}{1080}
=-7/20
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(189)+189}{2*540}=\frac{0}{1080}
=0
$