(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+48z-27=0

a = -5; b = 48; c = -27;
Δ = b2-4ac
Δ = 482-4·(-5)·(-27)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-42}{2*-5}=\frac{-90}{-10}
=+9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+42}{2*-5}=\frac{-6}{-10}
=3/5
$