(8-z)(5z+3)=0

Solution for (8-z)(5z+3)=0 equation:

(8-z)(5z+3)=0

We add all the numbers together, and all the variables

(-1z+8)(5z+3)=0

We multiply parentheses ..

(-5z^2-3z+40z+24)=0

We get rid of parentheses

-5z^2-3z+40z+24=0

We add all the numbers together, and all the variables

-5z^2+37z+24=0

a = -5; b = 37; c = +24;
Δ = b2-4ac
Δ = 372-4·(-5)·24
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-43}{2*-5}=\frac{-80}{-10}
=+8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+43}{2*-5}=\frac{6}{-10}
=-3/5
$