-1/2*12v-20+4=-12-8v

Solution for -1/2*12v-20+4=-12-8v equation:

-1/2*12v-20+4=-12-8v

We move all terms to the left:

-1/2*12v-20+4-(-12-8v)=0


Domain of the equation: 2*12v!=0

v!=0/1

v!=0

v∈R


We add all the numbers together, and all the variables

-1/2*12v-(-8v-12)-20+4=0

We add all the numbers together, and all the variables

-1/2*12v-(-8v-12)-16=0

We get rid of parentheses

-1/2*12v+8v+12-16=0

We multiply all the terms by the denominator


8v*2*12v+12*2*12v-16*2*12v-1=0

Wy multiply elements

192v^2*1+288v*1-384v*1-1=0

Wy multiply elements

192v^2+288v-384v-1=0

We add all the numbers together, and all the variables

192v^2-96v-1=0

a = 192; b = -96; c = -1;
Δ = b2-4ac
Δ = -962-4·192·(-1)
Δ = 9984
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:

$\sqrt{\Delta}=\sqrt{9984}=\sqrt{256*39}=\sqrt{256}*\sqrt{39}=16\sqrt{39}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-16\sqrt{39}}{2*192}=\frac{96-16\sqrt{39}}{384}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+16\sqrt{39}}{2*192}=\frac{96+16\sqrt{39}}{384}
$