a^2=-80a

Solution for a^2=-80a equation:

a^2=-80a

We move all terms to the left:

a^2-(-80a)=0

We get rid of parentheses

a^2+80a=0

a = 1; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·1·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-80}{2*1}=\frac{-160}{2}
=-80
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*1}=\frac{0}{2}
=0
$