3(4n-1)(4n+3)=48n

Solution for 3(4n-1)(4n+3)=48n equation:

3(4n-1)(4n+3)=48n

We move all terms to the left:

3(4n-1)(4n+3)-(48n)=0

We add all the numbers together, and all the variables

-48n+3(4n-1)(4n+3)=0

We multiply parentheses ..

3(+16n^2+12n-4n-3)-48n=0

We multiply parentheses

48n^2+36n-12n-48n-9=0

We add all the numbers together, and all the variables

48n^2-24n-9=0

a = 48; b = -24; c = -9;
Δ = b2-4ac
Δ = -242-4·48·(-9)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-48}{2*48}=\frac{-24}{96}
=-1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+48}{2*48}=\frac{72}{96}
=3/4
$