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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+4z^2+28z-1z-7)=0

We get rid of parentheses

4z^2+28z-1z-7=0

We add all the numbers together, and all the variables

4z^2+27z-7=0

a = 4; b = 27; c = -7;
Δ = b2-4ac
Δ = 272-4·4·(-7)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-29}{2*4}=\frac{-56}{8}
=-7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+29}{2*4}=\frac{2}{8}
=1/4
$