3v+6=1/2v-2

Solution for 3v+6=1/2v-2 equation:

3v+6=1/2v-2

We move all terms to the left:

3v+6-(1/2v-2)=0


Domain of the equation: 2v-2)!=0

v∈R


We get rid of parentheses

3v-1/2v+2+6=0

We multiply all the terms by the denominator


3v*2v+2*2v+6*2v-1=0

Wy multiply elements

6v^2+4v+12v-1=0

We add all the numbers together, and all the variables

6v^2+16v-1=0

a = 6; b = 16; c = -1;
Δ = b2-4ac
Δ = 162-4·6·(-1)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{70}}{2*6}=\frac{-16-2\sqrt{70}}{12}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{70}}{2*6}=\frac{-16+2\sqrt{70}}{12}
$