-4/3v+4/5=-2/5v-2

Solution for -4/3v+4/5=-2/5v-2 equation:

-4/3v+4/5=-2/5v-2

We move all terms to the left:

-4/3v+4/5-(-2/5v-2)=0


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R



Domain of the equation: 5v-2)!=0

v∈R


We get rid of parentheses

-4/3v+2/5v+2+4/5=0

We calculate fractions


300v^2/375v^2+(-500v)/375v^2+150v/375v^2+2=0

We multiply all the terms by the denominator


300v^2+(-500v)+150v+2*375v^2=0

We add all the numbers together, and all the variables

300v^2+150v+(-500v)+2*375v^2=0

Wy multiply elements

300v^2+750v^2+150v+(-500v)=0

We get rid of parentheses

300v^2+750v^2+150v-500v=0

We add all the numbers together, and all the variables

1050v^2-350v=0

a = 1050; b = -350; c = 0;
Δ = b2-4ac
Δ = -3502-4·1050·0
Δ = 122500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{122500}=350$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-350}{2*1050}=\frac{0}{2100}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+350}{2*1050}=\frac{700}{2100}
=1/3
$