(5z+4)(8-z)=0

Solution for (5z+4)(8-z)=0 equation:

(5z+4)(8-z)=0

We add all the numbers together, and all the variables

(5z+4)(-1z+8)=0

We multiply parentheses ..

(-5z^2+40z-4z+32)=0

We get rid of parentheses

-5z^2+40z-4z+32=0

We add all the numbers together, and all the variables

-5z^2+36z+32=0

a = -5; b = 36; c = +32;
Δ = b2-4ac
Δ = 362-4·(-5)·32
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{-(36)-44}{2*-5}=\frac{-80}{-10}
=+8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+44}{2*-5}=\frac{8}{-10}
=-4/5
$