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9n^2-9n-176=0
a = 9; b = -9; c = -176;
Δ = b2-4ac
Δ = -92-4·9·(-176)
Δ = 6417
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6417}=\sqrt{9*713}=\sqrt{9}*\sqrt{713}=3\sqrt{713}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{713}}{2*9}=\frac{9-3\sqrt{713}}{18} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{713}}{2*9}=\frac{9+3\sqrt{713}}{18} $
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