n2-16n=12

Solution for n2-16n=12 equation:

n2-16n=12

We move all terms to the left:

n2-16n-(12)=0

We add all the numbers together, and all the variables

n^2-16n-12=0

a = 1; b = -16; c = -12;
Δ = b2-4ac
Δ = -162-4·1·(-12)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{19}}{2*1}=\frac{16-4\sqrt{19}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{19}}{2*1}=\frac{16+4\sqrt{19}}{2}
$