4n^2-16n-12=n^2

Solution for 4n^2-16n-12=n^2 equation:

4n^2-16n-12=n^2

We move all terms to the left:

4n^2-16n-12-(n^2)=0

determiningTheFunctionDomain
4n^2-n^2-16n-12=0

We add all the numbers together, and all the variables

3n^2-16n-12=0

a = 3; b = -16; c = -12;
Δ = b2-4ac
Δ = -162-4·3·(-12)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-20}{2*3}=\frac{-4}{6}
=-2/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+20}{2*3}=\frac{36}{6}
=6
$