5w^2=-8w

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

5w^2=-8w

We move all terms to the left:

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

We get rid of parentheses

5w^2+8w=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:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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