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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

-1z^2+7z+z-7=0

We add all the numbers together, and all the variables

-1z^2+8z-7=0

a = -1; b = 8; c = -7;
Δ = b2-4ac
Δ = 82-4·(-1)·(-7)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6}{2*-1}=\frac{-14}{-2}
=+7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6}{2*-1}=\frac{-2}{-2}
=1
$