(5z-1)(9z)=0

Solution for (5z-1)(9z)=0 equation:

(5z-1)(9z)=0

We multiply parentheses

45z^2-9z=0

a = 45; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·45·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*45}=\frac{0}{90}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*45}=\frac{18}{90}
=1/5
$