-7/2v+2/3=-2/3v-4

Solution for -7/2v+2/3=-2/3v-4 equation:

-7/2v+2/3=-2/3v-4

We move all terms to the left:

-7/2v+2/3-(-2/3v-4)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 3v-4)!=0

v∈R


We get rid of parentheses

-7/2v+2/3v+4+2/3=0

We calculate fractions


(-189v)/54v^2+4v/54v^2+4v/54v^2+4=0

We multiply all the terms by the denominator


(-189v)+4v+4v+4*54v^2=0

We add all the numbers together, and all the variables

8v+(-189v)+4*54v^2=0

Wy multiply elements

216v^2+8v+(-189v)=0

We get rid of parentheses

216v^2+8v-189v=0

We add all the numbers together, and all the variables

216v^2-181v=0

a = 216; b = -181; c = 0;
Δ = b2-4ac
Δ = -1812-4·216·0
Δ = 32761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32761}=181$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-181)-181}{2*216}=\frac{0}{432}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-181)+181}{2*216}=\frac{362}{432}
=181/216
$