5z(5z+1)=0

Solution for 5z(5z+1)=0 equation:

5z(5z+1)=0

We multiply parentheses

25z^2+5z=0

a = 25; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·25·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*25}=\frac{-10}{50}
=-1/5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*25}=\frac{0}{50}
=0
$