(8-z)(2z-1)=0

Solution for (8-z)(2z-1)=0 equation:

(8-z)(2z-1)=0

We add all the numbers together, and all the variables

(-1z+8)(2z-1)=0

We multiply parentheses ..

(-2z^2+z+16z-8)=0

We get rid of parentheses

-2z^2+z+16z-8=0

We add all the numbers together, and all the variables

-2z^2+17z-8=0

a = -2; b = 17; c = -8;
Δ = b2-4ac
Δ = 172-4·(-2)·(-8)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-15}{2*-2}=\frac{-32}{-4}
=+8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+15}{2*-2}=\frac{-2}{-4}
=1/2
$