n(n-1)=650

Solution for n(n-1)=650 equation:

n(n-1)=650

We move all terms to the left:

n(n-1)-(650)=0

We multiply parentheses

n^2-1n-650=0

a = 1; b = -1; c = -650;
Δ = b2-4ac
Δ = -12-4·1·(-650)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-51}{2*1}=\frac{-50}{2}
=-25
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+51}{2*1}=\frac{52}{2}
=26
$