(s-1)(s-5)=0

Solution for (s-1)(s-5)=0 equation:

(s-1)(s-5)=0

We multiply parentheses ..

(+s^2-5s-1s+5)=0

We get rid of parentheses

s^2-5s-1s+5=0

We add all the numbers together, and all the variables

s^2-6s+5=0

a = 1; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·1·5
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4}{2*1}=\frac{2}{2}
=1
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4}{2*1}=\frac{10}{2}
=5
$