8v=4v2-4

Solution for 8v=4v2-4 equation:

8v=4v^2-4

We move all terms to the left:

8v-(4v^2-4)=0

We get rid of parentheses

-4v^2+8v+4=0

a = -4; b = 8; c = +4;
Δ = b2-4ac
Δ = 82-4·(-4)·4
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{2}}{2*-4}=\frac{-8-8\sqrt{2}}{-8}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{2}}{2*-4}=\frac{-8+8\sqrt{2}}{-8}
$