(7+z)(5z+8)=0

Solution for (7+z)(5z+8)=0 equation:

(7+z)(5z+8)=0

We add all the numbers together, and all the variables

(z+7)(5z+8)=0

We multiply parentheses ..

(+5z^2+8z+35z+56)=0

We get rid of parentheses

5z^2+8z+35z+56=0

We add all the numbers together, and all the variables

5z^2+43z+56=0

a = 5; b = 43; c = +56;
Δ = b2-4ac
Δ = 432-4·5·56
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-27}{2*5}=\frac{-70}{10}
=-7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+27}{2*5}=\frac{-16}{10}
=-1+3/5
$