0=151-48n+3n^2

Solution for 0=151-48n+3n^2 equation:

0=151-48n+3n^2

We move all terms to the left:

0-(151-48n+3n^2)=0

We add all the numbers together, and all the variables

-(151-48n+3n^2)=0

We get rid of parentheses

-3n^2+48n-151=0

a = -3; b = 48; c = -151;
Δ = b2-4ac
Δ = 482-4·(-3)·(-151)
Δ = 492
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:

$\sqrt{\Delta}=\sqrt{492}=\sqrt{4*123}=\sqrt{4}*\sqrt{123}=2\sqrt{123}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-2\sqrt{123}}{2*-3}=\frac{-48-2\sqrt{123}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+2\sqrt{123}}{2*-3}=\frac{-48+2\sqrt{123}}{-6}
$