n^2-1+6n+6n=0

Solution for n^2-1+6n+6n=0 equation:

n^2-1+6n+6n=0

We add all the numbers together, and all the variables

n^2+12n-1=0

a = 1; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·1·(-1)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{37}}{2*1}=\frac{-12-2\sqrt{37}}{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{37}}{2*1}=\frac{-12+2\sqrt{37}}{2}
$