6n(n-1)+4=36

Solution for 6n(n-1)+4=36 equation:

6n(n-1)+4=36

We move all terms to the left:

6n(n-1)+4-(36)=0

We add all the numbers together, and all the variables

6n(n-1)-32=0

We multiply parentheses

6n^2-6n-32=0

a = 6; b = -6; c = -32;
Δ = b2-4ac
Δ = -62-4·6·(-32)
Δ = 804
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:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{201}}{2*6}=\frac{6-2\sqrt{201}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{201}}{2*6}=\frac{6+2\sqrt{201}}{12}
$