-48=-6(2n+8)12n

Solution for -48=-6(2n+8)12n equation:

-48=-6(2n+8)12n

We move all terms to the left:

-48-(-6(2n+8)12n)=0


We calculate terms in parentheses: -(-6(2n+8)12n), so:

-6(2n+8)12n

We multiply parentheses

-144n^2-576n

Back to the equation:

-(-144n^2-576n)


We get rid of parentheses

144n^2+576n-48=0

a = 144; b = 576; c = -48;
Δ = b2-4ac
Δ = 5762-4·144·(-48)
Δ = 359424
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:

$\sqrt{\Delta}=\sqrt{359424}=\sqrt{9216*39}=\sqrt{9216}*\sqrt{39}=96\sqrt{39}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(576)-96\sqrt{39}}{2*144}=\frac{-576-96\sqrt{39}}{288}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(576)+96\sqrt{39}}{2*144}=\frac{-576+96\sqrt{39}}{288}
$