3n(3n-3)=104

Solution for 3n(3n-3)=104 equation:

3n(3n-3)=104

We move all terms to the left:

3n(3n-3)-(104)=0

We multiply parentheses

9n^2-9n-104=0

a = 9; b = -9; c = -104;
Δ = b2-4ac
Δ = -92-4·9·(-104)
Δ = 3825
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:

$\sqrt{\Delta}=\sqrt{3825}=\sqrt{225*17}=\sqrt{225}*\sqrt{17}=15\sqrt{17}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15\sqrt{17}}{2*9}=\frac{9-15\sqrt{17}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15\sqrt{17}}{2*9}=\frac{9+15\sqrt{17}}{18}
$