9n^2-6n=1

Solution for 9n^2-6n=1 equation:

9n^2-6n=1

We move all terms to the left:

9n^2-6n-(1)=0

a = 9; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·9·(-1)
Δ = 72
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{2}}{2*9}=\frac{6-6\sqrt{2}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{2}}{2*9}=\frac{6+6\sqrt{2}}{18}
$