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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-3z^2-8z+15z+40)=0

We get rid of parentheses

-3z^2-8z+15z+40=0

We add all the numbers together, and all the variables

-3z^2+7z+40=0

a = -3; b = 7; c = +40;
Δ = b2-4ac
Δ = 72-4·(-3)·40
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-23}{2*-3}=\frac{-30}{-6}
=+5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+23}{2*-3}=\frac{16}{-6}
=-2+2/3
$