12+4n=4n(n+7)

Solution for 12+4n=4n(n+7) equation:

12+4n=4n(n+7)

We move all terms to the left:

12+4n-(4n(n+7))=0


We calculate terms in parentheses: -(4n(n+7)), so:

4n(n+7)

We multiply parentheses

4n^2+28n

Back to the equation:

-(4n^2+28n)


We get rid of parentheses

-4n^2+4n-28n+12=0

We add all the numbers together, and all the variables

-4n^2-24n+12=0

a = -4; b = -24; c = +12;
Δ = b2-4ac
Δ = -242-4·(-4)·12
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-16\sqrt{3}}{2*-4}=\frac{24-16\sqrt{3}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+16\sqrt{3}}{2*-4}=\frac{24+16\sqrt{3}}{-8}
$