n*(n-1)=156

Solution for n*(n-1)=156 equation:

n(n-1)=156

We move all terms to the left:

n(n-1)-(156)=0

We multiply parentheses

n^2-1n-156=0

a = 1; b = -1; c = -156;
Δ = b2-4ac
Δ = -12-4·1·(-156)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-25}{2*1}=\frac{-24}{2}
=-12
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+25}{2*1}=\frac{26}{2}
=13
$