5/9v-1/3=2/3v+13

Solution for 5/9v-1/3=2/3v+13 equation:

5/9v-1/3=2/3v+13

We move all terms to the left:

5/9v-1/3-(2/3v+13)=0


Domain of the equation: 9v!=0

v!=0/9

v!=0

v∈R



Domain of the equation: 3v+13)!=0

v∈R


We get rid of parentheses

5/9v-2/3v-13-1/3=0

We calculate fractions


135v/243v^2+(-18v)/243v^2+(-9v)/243v^2-13=0

We multiply all the terms by the denominator


135v+(-18v)+(-9v)-13*243v^2=0

Wy multiply elements

-3159v^2+135v+(-18v)+(-9v)=0

We get rid of parentheses

-3159v^2+135v-18v-9v=0

We add all the numbers together, and all the variables

-3159v^2+108v=0

a = -3159; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·(-3159)·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*-3159}=\frac{-216}{-6318}
=4/117
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*-3159}=\frac{0}{-6318}
=0
$