9k^2-k=1

Solution for 9k^2-k=1 equation:

9k^2-k=1

We move all terms to the left:

9k^2-k-(1)=0

We add all the numbers together, and all the variables

9k^2-1k-1=0

a = 9; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·9·(-1)
Δ = 37
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{37}}{2*9}=\frac{1-\sqrt{37}}{18}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{37}}{2*9}=\frac{1+\sqrt{37}}{18}
$