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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-4z^2+28z-2z+14)=0

We get rid of parentheses

-4z^2+28z-2z+14=0

We add all the numbers together, and all the variables

-4z^2+26z+14=0

a = -4; b = 26; c = +14;
Δ = b2-4ac
Δ = 262-4·(-4)·14
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{-(26)-30}{2*-4}=\frac{-56}{-8}
=+7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+30}{2*-4}=\frac{4}{-8}
=-1/2
$