12v^2-6v=8

Solution for 12v^2-6v=8 equation:

12v^2-6v=8

We move all terms to the left:

12v^2-6v-(8)=0

a = 12; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·12·(-8)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{105}}{2*12}=\frac{6-2\sqrt{105}}{24}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{105}}{2*12}=\frac{6+2\sqrt{105}}{24}
$