8v^2=-64v

Solution for 8v^2=-64v equation:

8v^2=-64v

We move all terms to the left:

8v^2-(-64v)=0

We get rid of parentheses

8v^2+64v=0

a = 8; b = 64; c = 0;
Δ = b2-4ac
Δ = 642-4·8·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-64}{2*8}=\frac{-128}{16}
=-8
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+64}{2*8}=\frac{0}{16}
=0
$