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n^2-8n-65=0
a = 1; b = -8; c = -65;
Δ = b2-4ac
Δ = -82-4·1·(-65)
Δ = 324
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{324}=18$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-18}{2*1}=\frac{-10}{2} =-5 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+18}{2*1}=\frac{26}{2} =13 $
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