(9-z)(5z+3)=0

Solution for (9-z)(5z+3)=0 equation:

(9-z)(5z+3)=0

We add all the numbers together, and all the variables

(-1z+9)(5z+3)=0

We multiply parentheses ..

(-5z^2-3z+45z+27)=0

We get rid of parentheses

-5z^2-3z+45z+27=0

We add all the numbers together, and all the variables

-5z^2+42z+27=0

a = -5; b = 42; c = +27;
Δ = b2-4ac
Δ = 422-4·(-5)·27
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-48}{2*-5}=\frac{-90}{-10}
=+9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+48}{2*-5}=\frac{6}{-10}
=-3/5
$