v-8/2v=6

Solution for v-8/2v=6 equation:

v-8/2v=6

We move all terms to the left:

v-8/2v-(6)=0


Domain of the equation: 2v!=0

v!=0/2

v!=0

v∈R


We multiply all the terms by the denominator


v*2v-6*2v-8=0

Wy multiply elements

2v^2-12v-8=0

a = 2; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·2·(-8)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{13}}{2*2}=\frac{12-4\sqrt{13}}{4}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{13}}{2*2}=\frac{12+4\sqrt{13}}{4}
$