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18n^2-36n-24=0
a = 18; b = -36; c = -24;
Δ = b2-4ac
Δ = -362-4·18·(-24)
Δ = 3024
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{21}}{2*18}=\frac{36-12\sqrt{21}}{36} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{21}}{2*18}=\frac{36+12\sqrt{21}}{36} $
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