27k^2-9k+9k-k=0

Solution for 27k^2-9k+9k-k=0 equation:

27k^2-9k+9k-k=0

We add all the numbers together, and all the variables

27k^2-1k=0

a = 27; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·27·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*27}=\frac{0}{54}
=0
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*27}=\frac{2}{54}
=1/27
$