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8+81n^2=33
We move all terms to the left:
8+81n^2-(33)=0
We add all the numbers together, and all the variables
81n^2-25=0
a = 81; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·81·(-25)
Δ = 8100
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{8100}=90$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-90}{2*81}=\frac{-90}{162} =-5/9 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+90}{2*81}=\frac{90}{162} =5/9 $
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