(8k-1)(k-1)=0

Solution for (8k-1)(k-1)=0 equation:

(8k-1)(k-1)=0

We multiply parentheses ..

(+8k^2-8k-1k+1)=0

We get rid of parentheses

8k^2-8k-1k+1=0

We add all the numbers together, and all the variables

8k^2-9k+1=0

a = 8; b = -9; c = +1;
Δ = b2-4ac
Δ = -92-4·8·1
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-7}{2*8}=\frac{2}{16}
=1/8
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+7}{2*8}=\frac{16}{16}
=1
$