w(w+1)=100

Solution for w(w+1)=100 equation:

w(w+1)=100

We move all terms to the left:

w(w+1)-(100)=0

We multiply parentheses

w^2+w-100=0

a = 1; b = 1; c = -100;
Δ = b2-4ac
Δ = 12-4·1·(-100)
Δ = 401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{401}}{2*1}=\frac{-1-\sqrt{401}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{401}}{2*1}=\frac{-1+\sqrt{401}}{2}
$