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9n^2-27n-77=0
a = 9; b = -27; c = -77;
Δ = b2-4ac
Δ = -272-4·9·(-77)
Δ = 3501
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3501}=\sqrt{9*389}=\sqrt{9}*\sqrt{389}=3\sqrt{389}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{389}}{2*9}=\frac{27-3\sqrt{389}}{18} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{389}}{2*9}=\frac{27+3\sqrt{389}}{18} $
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