33n^2-33n-120=0

Solution for 33n^2-33n-120=0 equation:

33n^2-33n-120=0

a = 33; b = -33; c = -120;
Δ = b2-4ac
Δ = -332-4·33·(-120)
Δ = 16929
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:

$\sqrt{\Delta}=\sqrt{16929}=\sqrt{81*209}=\sqrt{81}*\sqrt{209}=9\sqrt{209}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-9\sqrt{209}}{2*33}=\frac{33-9\sqrt{209}}{66}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+9\sqrt{209}}{2*33}=\frac{33+9\sqrt{209}}{66}
$