(8-z)(2z-3)=0

Solution for (8-z)(2z-3)=0 equation:

(8-z)(2z-3)=0

We add all the numbers together, and all the variables

(-1z+8)(2z-3)=0

We multiply parentheses ..

(-2z^2+3z+16z-24)=0

We get rid of parentheses

-2z^2+3z+16z-24=0

We add all the numbers together, and all the variables

-2z^2+19z-24=0

a = -2; b = 19; c = -24;
Δ = b2-4ac
Δ = 192-4·(-2)·(-24)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-13}{2*-2}=\frac{-32}{-4}
=+8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+13}{2*-2}=\frac{-6}{-4}
=1+1/2
$