n*(2n-1)=512

Solution for n*(2n-1)=512 equation:

n(2n-1)=512

We move all terms to the left:

n(2n-1)-(512)=0

We multiply parentheses

2n^2-1n-512=0

a = 2; b = -1; c = -512;
Δ = b2-4ac
Δ = -12-4·2·(-512)
Δ = 4097
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{4097}}{2*2}=\frac{1-\sqrt{4097}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{4097}}{2*2}=\frac{1+\sqrt{4097}}{4}
$