2/v-3v-2=0

Solution for 2/v-3v-2=0 equation:

2/v-3v-2=0


Domain of the equation: v!=0

v∈R


We add all the numbers together, and all the variables

-3v+2/v-2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -3; b = -2; c = +2;
Δ = b2-4ac
Δ = -22-4·(-3)·2
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{7}}{2*-3}=\frac{2-2\sqrt{7}}{-6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{7}}{2*-3}=\frac{2+2\sqrt{7}}{-6}
$