6n(n-1)+1=73

Solution for 6n(n-1)+1=73 equation:

6n(n-1)+1=73

We move all terms to the left:

6n(n-1)+1-(73)=0

We add all the numbers together, and all the variables

6n(n-1)-72=0

We multiply parentheses

6n^2-6n-72=0

a = 6; b = -6; c = -72;
Δ = b2-4ac
Δ = -62-4·6·(-72)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-42}{2*6}=\frac{-36}{12}
=-3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+42}{2*6}=\frac{48}{12}
=4
$