(1-z)(4z-7)=0

Solution for (1-z)(4z-7)=0 equation:

(1-z)(4z-7)=0

We add all the numbers together, and all the variables

(-1z+1)(4z-7)=0

We multiply parentheses ..

(-4z^2+7z+4z-7)=0

We get rid of parentheses

-4z^2+7z+4z-7=0

We add all the numbers together, and all the variables

-4z^2+11z-7=0

a = -4; b = 11; c = -7;
Δ = b2-4ac
Δ = 112-4·(-4)·(-7)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3}{2*-4}=\frac{-14}{-8}
=1+3/4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3}{2*-4}=\frac{-8}{-8}
=1
$