12-3(n-1)n=1

Solution for 12-3(n-1)n=1 equation:

12-3(n-1)n=1

We move all terms to the left:

12-3(n-1)n-(1)=0

We add all the numbers together, and all the variables

-3(n-1)n+11=0

We multiply parentheses

-3n^2+3n+11=0

a = -3; b = 3; c = +11;
Δ = b2-4ac
Δ = 32-4·(-3)·11
Δ = 141
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{141}}{2*-3}=\frac{-3-\sqrt{141}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{141}}{2*-3}=\frac{-3+\sqrt{141}}{-6}
$