6n^2+72n+192=1

Solution for 6n^2+72n+192=1 equation:

6n^2+72n+192=1

We move all terms to the left:

6n^2+72n+192-(1)=0

We add all the numbers together, and all the variables

6n^2+72n+191=0

a = 6; b = 72; c = +191;
Δ = b2-4ac
Δ = 722-4·6·191
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-10\sqrt{6}}{2*6}=\frac{-72-10\sqrt{6}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+10\sqrt{6}}{2*6}=\frac{-72+10\sqrt{6}}{12}
$