-1/2v+11/6v=2/9

Solution for -1/2v+11/6v=2/9 equation:

-1/2v+11/6v=2/9

We move all terms to the left:

-1/2v+11/6v-(2/9)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R



Domain of the equation: 6v!=0

v!=0/6

v!=0

v∈R


We add all the numbers together, and all the variables

-1/2v+11/6v-(+2/9)=0

We get rid of parentheses

-1/2v+11/6v-2/9=0

We calculate fractions


(-144v^2)/972v^2+(-486v)/972v^2+1782v/972v^2=0

We multiply all the terms by the denominator


(-144v^2)+(-486v)+1782v=0

We add all the numbers together, and all the variables

(-144v^2)+1782v+(-486v)=0

We get rid of parentheses

-144v^2+1782v-486v=0

We add all the numbers together, and all the variables

-144v^2+1296v=0

a = -144; b = 1296; c = 0;
Δ = b2-4ac
Δ = 12962-4·(-144)·0
Δ = 1679616
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1679616}=1296$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1296)-1296}{2*-144}=\frac{-2592}{-288}
=+9
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1296)+1296}{2*-144}=\frac{0}{-288}
=0
$