5z(z+2)=0

Solution for 5z(z+2)=0 equation:

5z(z+2)=0

We multiply parentheses

5z^2+10z=0

a = 5; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·5·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*5}=\frac{-20}{10}
=-2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*5}=\frac{0}{10}
=0
$