3n^2-3n-1728=0

Solution for 3n^2-3n-1728=0 equation:

3n^2-3n-1728=0

a = 3; b = -3; c = -1728;
Δ = b2-4ac
Δ = -32-4·3·(-1728)
Δ = 20745
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:

$\sqrt{\Delta}=\sqrt{20745}=\sqrt{9*2305}=\sqrt{9}*\sqrt{2305}=3\sqrt{2305}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{2305}}{2*3}=\frac{3-3\sqrt{2305}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{2305}}{2*3}=\frac{3+3\sqrt{2305}}{6}
$