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4n^2-8n-11=0
a = 4; b = -8; c = -11;
Δ = b2-4ac
Δ = -82-4·4·(-11)
Δ = 240
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{15}}{2*4}=\frac{8-4\sqrt{15}}{8} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{15}}{2*4}=\frac{8+4\sqrt{15}}{8} $
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