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3n^2+9n=86.75
We move all terms to the left:
3n^2+9n-(86.75)=0
We add all the numbers together, and all the variables
3n^2+9n-86.75=0
a = 3; b = 9; c = -86.75;
Δ = b2-4ac
Δ = 92-4·3·(-86.75)
Δ = 1122
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{1122}}{2*3}=\frac{-9-\sqrt{1122}}{6} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{1122}}{2*3}=\frac{-9+\sqrt{1122}}{6} $
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