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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+5z^2+40z-7z-56)=0

We get rid of parentheses

5z^2+40z-7z-56=0

We add all the numbers together, and all the variables

5z^2+33z-56=0

a = 5; b = 33; c = -56;
Δ = b2-4ac
Δ = 332-4·5·(-56)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-47}{2*5}=\frac{-80}{10}
=-8
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+47}{2*5}=\frac{14}{10}
=1+2/5
$