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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4z^2+27z+40=0

a = -4; b = 27; c = +40;
Δ = b2-4ac
Δ = 272-4·(-4)·40
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{-(27)-37}{2*-4}=\frac{-64}{-8}
=+8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+37}{2*-4}=\frac{10}{-8}
=-1+1/4
$