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n(n-3)/2=70
We move all terms to the left:
n(n-3)/2-(70)=0
We multiply all the terms by the denominator
n(n-3)-70*2=0
We add all the numbers together, and all the variables
n(n-3)-140=0
We multiply parentheses
n^2-3n-140=0
a = 1; b = -3; c = -140;
Δ = b2-4ac
Δ = -32-4·1·(-140)
Δ = 569
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{-(-3)-\sqrt{569}}{2*1}=\frac{3-\sqrt{569}}{2} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{569}}{2*1}=\frac{3+\sqrt{569}}{2} $
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