n(n-1)=600

Solution for n(n-1)=600 equation:

n(n-1)=600

We move all terms to the left:

n(n-1)-(600)=0

We multiply parentheses

n^2-1n-600=0

a = 1; b = -1; c = -600;
Δ = b2-4ac
Δ = -12-4·1·(-600)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-49}{2*1}=\frac{-48}{2}
=-24
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+49}{2*1}=\frac{50}{2}
=25
$