v-6/v-1=6/3

Solution for v-6/v-1=6/3 equation:

v-6/v-1=6/3

We move all terms to the left:

v-6/v-1-(6/3)=0


Domain of the equation: v!=0

v∈R


We add all the numbers together, and all the variables

v-6/v-1-2=0

We add all the numbers together, and all the variables

v-6/v-3=0

We multiply all the terms by the denominator


v*v-3*v-6=0

We add all the numbers together, and all the variables

-3v+v*v-6=0

Wy multiply elements

v^2-3v-6=0

a = 1; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·1·(-6)
Δ = 33
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{-(-3)-\sqrt{33}}{2*1}=\frac{3-\sqrt{33}}{2}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33}}{2*1}=\frac{3+\sqrt{33}}{2}
$