48n-3n^2=9

Solution for 48n-3n^2=9 equation:

48n-3n^2=9

We move all terms to the left:

48n-3n^2-(9)=0

a = -3; b = 48; c = -9;
Δ = b2-4ac
Δ = 482-4·(-3)·(-9)
Δ = 2196
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:

$\sqrt{\Delta}=\sqrt{2196}=\sqrt{36*61}=\sqrt{36}*\sqrt{61}=6\sqrt{61}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{61}}{2*-3}=\frac{-48-6\sqrt{61}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{61}}{2*-3}=\frac{-48+6\sqrt{61}}{-6}
$