-5(z-7)(-z+1)=0

Solution for -5(z-7)(-z+1)=0 equation:

-5(z-7)(-z+1)=0

We add all the numbers together, and all the variables

-5(z-7)(-1z+1)=0

We multiply parentheses ..

-5(-1z^2+z+7z-7)=0

We multiply parentheses

5z^2-5z-35z+35=0

We add all the numbers together, and all the variables

5z^2-40z+35=0

a = 5; b = -40; c = +35;
Δ = b2-4ac
Δ = -402-4·5·35
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-30}{2*5}=\frac{10}{10}
=1
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+30}{2*5}=\frac{70}{10}
=7
$