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

Solution for (4-z)(2z+7)=0 equation:

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

We add all the numbers together, and all the variables

(-1z+4)(2z+7)=0

We multiply parentheses ..

(-2z^2-7z+8z+28)=0

We get rid of parentheses

-2z^2-7z+8z+28=0

We add all the numbers together, and all the variables

-2z^2+z+28=0

a = -2; b = 1; c = +28;
Δ = b2-4ac
Δ = 12-4·(-2)·28
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-15}{2*-2}=\frac{-16}{-4}
=+4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+15}{2*-2}=\frac{14}{-4}
=-3+1/2
$