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

Solution for 5(z-4)(-z-1)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

5(-1z^2-1z+4z+4)=0

We multiply parentheses

-5z^2-5z+20z+20=0

We add all the numbers together, and all the variables

-5z^2+15z+20=0

a = -5; b = 15; c = +20;
Δ = b2-4ac
Δ = 152-4·(-5)·20
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-25}{2*-5}=\frac{-40}{-10}
=+4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+25}{2*-5}=\frac{10}{-10}
=-1
$