(9-z)(5z-8)=0

Solution for (9-z)(5z-8)=0 equation:

(9-z)(5z-8)=0

We add all the numbers together, and all the variables

(-1z+9)(5z-8)=0

We multiply parentheses ..

(-5z^2+8z+45z-72)=0

We get rid of parentheses

-5z^2+8z+45z-72=0

We add all the numbers together, and all the variables

-5z^2+53z-72=0

a = -5; b = 53; c = -72;
Δ = b2-4ac
Δ = 532-4·(-5)·(-72)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(53)-37}{2*-5}=\frac{-90}{-10}
=+9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(53)+37}{2*-5}=\frac{-16}{-10}
=1+3/5
$