6n(n-1)+1=13

Solution for 6n(n-1)+1=13 equation:

6n(n-1)+1=13

We move all terms to the left:

6n(n-1)+1-(13)=0

We add all the numbers together, and all the variables

6n(n-1)-12=0

We multiply parentheses

6n^2-6n-12=0

a = 6; b = -6; c = -12;
Δ = b2-4ac
Δ = -62-4·6·(-12)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*6}=\frac{-12}{12}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*6}=\frac{24}{12}
=2
$