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x(x+1)/2=200
We move all terms to the left:
x(x+1)/2-(200)=0
We multiply all the terms by the denominator
x(x+1)-200*2=0
We add all the numbers together, and all the variables
x(x+1)-400=0
We multiply parentheses
x^2+x-400=0
a = 1; b = 1; c = -400;
Δ = b2-4ac
Δ = 12-4·1·(-400)
Δ = 1601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{1601}}{2*1}=\frac{-1-\sqrt{1601}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1601}}{2*1}=\frac{-1+\sqrt{1601}}{2} $
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