5v^2=-8v

Solution for 5v^2=-8v equation:

5v^2=-8v

We move all terms to the left:

5v^2-(-8v)=0

We get rid of parentheses

5v^2+8v=0

a = 5; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·5·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*5}=\frac{-16}{10}
=-1+3/5
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*5}=\frac{0}{10}
=0
$