(5+z)(4z+7)=0

Solution for (5+z)(4z+7)=0 equation:

(5+z)(4z+7)=0

We add all the numbers together, and all the variables

(z+5)(4z+7)=0

We multiply parentheses ..

(+4z^2+7z+20z+35)=0

We get rid of parentheses

4z^2+7z+20z+35=0

We add all the numbers together, and all the variables

4z^2+27z+35=0

a = 4; b = 27; c = +35;
Δ = b2-4ac
Δ = 272-4·4·35
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-13}{2*4}=\frac{-40}{8}
=-5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+13}{2*4}=\frac{-14}{8}
=-1+3/4
$