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

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

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5z^2+27z-56=0

a = 5; b = 27; c = -56;
Δ = b2-4ac
Δ = 272-4·5·(-56)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-43}{2*5}=\frac{-70}{10}
=-7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+43}{2*5}=\frac{16}{10}
=1+3/5
$