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n^2+12n-85=0
a = 1; b = 12; c = -85;
Δ = b2-4ac
Δ = 122-4·1·(-85)
Δ = 484
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{484}=22$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-22}{2*1}=\frac{-34}{2} =-17 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+22}{2*1}=\frac{10}{2} =5 $
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