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n(n-2)=240
We move all terms to the left:
n(n-2)-(240)=0
We multiply parentheses
n^2-2n-240=0
a = 1; b = -2; c = -240;
Δ = b2-4ac
Δ = -22-4·1·(-240)
Δ = 964
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{964}=\sqrt{4*241}=\sqrt{4}*\sqrt{241}=2\sqrt{241}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{241}}{2*1}=\frac{2-2\sqrt{241}}{2} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{241}}{2*1}=\frac{2+2\sqrt{241}}{2} $
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