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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-5z^2-1z+45z+9)=0

We get rid of parentheses

-5z^2-1z+45z+9=0

We add all the numbers together, and all the variables

-5z^2+44z+9=0

a = -5; b = 44; c = +9;
Δ = b2-4ac
Δ = 442-4·(-5)·9
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-46}{2*-5}=\frac{-90}{-10}
=+9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+46}{2*-5}=\frac{2}{-10}
=-1/5
$