-5z(3z-1)=0

Solution for -5z(3z-1)=0 equation:

-5z(3z-1)=0

We multiply parentheses

-15z^2+5z=0

a = -15; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-15)·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*-15}=\frac{-10}{-30}
=1/3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-15}=\frac{0}{-30}
=0
$