-1/6v-2/3=3/2v+4

Solution for -1/6v-2/3=3/2v+4 equation:

-1/6v-2/3=3/2v+4

We move all terms to the left:

-1/6v-2/3-(3/2v+4)=0


Domain of the equation: 6v!=0

v!=0/6

v!=0

v∈R



Domain of the equation: 2v+4)!=0

v∈R


We get rid of parentheses

-1/6v-3/2v-4-2/3=0

We calculate fractions


(-48v^2)/108v^2+(-18v)/108v^2+(-162v)/108v^2-4=0

We multiply all the terms by the denominator


(-48v^2)+(-18v)+(-162v)-4*108v^2=0

Wy multiply elements

(-48v^2)-432v^2+(-18v)+(-162v)=0

We get rid of parentheses

-48v^2-432v^2-18v-162v=0

We add all the numbers together, and all the variables

-480v^2-180v=0

a = -480; b = -180; c = 0;
Δ = b2-4ac
Δ = -1802-4·(-480)·0
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-180}{2*-480}=\frac{0}{-960}
=0
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+180}{2*-480}=\frac{360}{-960}
=-3/8
$