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4n^2-9n-18=6
We move all terms to the left:
4n^2-9n-18-(6)=0
We add all the numbers together, and all the variables
4n^2-9n-24=0
a = 4; b = -9; c = -24;
Δ = b2-4ac
Δ = -92-4·4·(-24)
Δ = 465
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{465}}{2*4}=\frac{9-\sqrt{465}}{8} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{465}}{2*4}=\frac{9+\sqrt{465}}{8} $
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