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n(n+1)=300
We move all terms to the left:
n(n+1)-(300)=0
We multiply parentheses
n^2+n-300=0
a = 1; b = 1; c = -300;
Δ = b2-4ac
Δ = 12-4·1·(-300)
Δ = 1201
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{1201}}{2*1}=\frac{-1-\sqrt{1201}}{2} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1201}}{2*1}=\frac{-1+\sqrt{1201}}{2} $
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