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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5z^2+46z-9=0

a = -5; b = 46; c = -9;
Δ = b2-4ac
Δ = 462-4·(-5)·(-9)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-44}{2*-5}=\frac{-90}{-10}
=+9
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+44}{2*-5}=\frac{-2}{-10}
=1/5
$