n+12=(6n)2

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

n+12=(6n)2

We move all terms to the left:

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

determiningTheFunctionDomain
n-6n2+12=0

We add all the numbers together, and all the variables

-6n^2+n+12=0

a = -6; b = 1; c = +12;
Δ = b2-4ac
Δ = 12-4·(-6)·12
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*-6}=\frac{-18}{-12}
=1+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*-6}=\frac{16}{-12}
=-1+1/3
$