3n2-1=12n+8

Solution for 3n2-1=12n+8 equation:

3n^2-1=12n+8

We move all terms to the left:

3n^2-1-(12n+8)=0

We get rid of parentheses

3n^2-12n-8-1=0

We add all the numbers together, and all the variables

3n^2-12n-9=0

a = 3; b = -12; c = -9;
Δ = b2-4ac
Δ = -122-4·3·(-9)
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{7}}{2*3}=\frac{12-6\sqrt{7}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{7}}{2*3}=\frac{12+6\sqrt{7}}{6}
$