(9k-9)(9k-1)=0

Solution for (9k-9)(9k-1)=0 equation:

(9k-9)(9k-1)=0

We multiply parentheses ..

(+81k^2-9k-81k+9)=0

We get rid of parentheses

81k^2-9k-81k+9=0

We add all the numbers together, and all the variables

81k^2-90k+9=0

a = 81; b = -90; c = +9;
Δ = b2-4ac
Δ = -902-4·81·9
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-72}{2*81}=\frac{18}{162}
=1/9
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+72}{2*81}=\frac{162}{162}
=1
$