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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+5z^2+25z+z+5)=0

We get rid of parentheses

5z^2+25z+z+5=0

We add all the numbers together, and all the variables

5z^2+26z+5=0

a = 5; b = 26; c = +5;
Δ = b2-4ac
Δ = 262-4·5·5
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-24}{2*5}=\frac{-50}{10}
=-5
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+24}{2*5}=\frac{-2}{10}
=-1/5
$