2/3v-7=v

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

2/3v-7=v

We move all terms to the left:

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


Domain of the equation: 3v!=0

v!=0/3

v!=0

v∈R


We add all the numbers together, and all the variables

-1v+2/3v-7=0

We multiply all the terms by the denominator


-1v*3v-7*3v+2=0

Wy multiply elements

-3v^2-21v+2=0

a = -3; b = -21; c = +2;
Δ = b2-4ac
Δ = -212-4·(-3)·2
Δ = 465
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{465}}{2*-3}=\frac{21-\sqrt{465}}{-6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{465}}{2*-3}=\frac{21+\sqrt{465}}{-6}
$