(8-z)(5z+2)=0

Solution for (8-z)(5z+2)=0 equation:

(8-z)(5z+2)=0

We add all the numbers together, and all the variables

(-1z+8)(5z+2)=0

We multiply parentheses ..

(-5z^2-2z+40z+16)=0

We get rid of parentheses

-5z^2-2z+40z+16=0

We add all the numbers together, and all the variables

-5z^2+38z+16=0

a = -5; b = 38; c = +16;
Δ = b2-4ac
Δ = 382-4·(-5)·16
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-42}{2*-5}=\frac{-80}{-10}
=+8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+42}{2*-5}=\frac{4}{-10}
=-2/5
$