6n(4n+4)=8(3+3n)

Solution for 6n(4n+4)=8(3+3n) equation:

6n(4n+4)=8(3+3n)

We move all terms to the left:

6n(4n+4)-(8(3+3n))=0

We add all the numbers together, and all the variables

6n(4n+4)-(8(3n+3))=0

We multiply parentheses

24n^2+24n-(8(3n+3))=0


We calculate terms in parentheses: -(8(3n+3)), so:

8(3n+3)

We multiply parentheses

24n+24

Back to the equation:

-(24n+24)


We get rid of parentheses

24n^2+24n-24n-24=0

We add all the numbers together, and all the variables

24n^2-24=0

a = 24; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·24·(-24)
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{-(0)-48}{2*24}=\frac{-48}{48}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48}{2*24}=\frac{48}{48}
=1
$