48=51n-3n^2

Solution for 48=51n-3n^2 equation:

48=51n-3n^2

We move all terms to the left:

48-(51n-3n^2)=0

We get rid of parentheses

3n^2-51n+48=0

a = 3; b = -51; c = +48;
Δ = b2-4ac
Δ = -512-4·3·48
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-45}{2*3}=\frac{6}{6}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+45}{2*3}=\frac{96}{6}
=16
$