(7-z)(5z+1)=0

Solution for (7-z)(5z+1)=0 equation:

(7-z)(5z+1)=0

We add all the numbers together, and all the variables

(-1z+7)(5z+1)=0

We multiply parentheses ..

(-5z^2-1z+35z+7)=0

We get rid of parentheses

-5z^2-1z+35z+7=0

We add all the numbers together, and all the variables

-5z^2+34z+7=0

a = -5; b = 34; c = +7;
Δ = b2-4ac
Δ = 342-4·(-5)·7
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-36}{2*-5}=\frac{-70}{-10}
=+7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+36}{2*-5}=\frac{2}{-10}
=-1/5
$