12v^2-8v=8

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

12v^2-8v=8

We move all terms to the left:

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

a = 12; b = -8; c = -8;
Δ = b2-4ac
Δ = -82-4·12·(-8)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{7}}{2*12}=\frac{8-8\sqrt{7}}{24}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{7}}{2*12}=\frac{8+8\sqrt{7}}{24}
$