(7z-1)(9z-5)=0

Solution for (7z-1)(9z-5)=0 equation:

(7z-1)(9z-5)=0

We multiply parentheses ..

(+63z^2-35z-9z+5)=0

We get rid of parentheses

63z^2-35z-9z+5=0

We add all the numbers together, and all the variables

63z^2-44z+5=0

a = 63; b = -44; c = +5;
Δ = b2-4ac
Δ = -442-4·63·5
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-26}{2*63}=\frac{18}{126}
=1/7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+26}{2*63}=\frac{70}{126}
=5/9
$