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9n^2-31+12=0
We add all the numbers together, and all the variables
9n^2-19=0
a = 9; b = 0; c = -19;
Δ = b2-4ac
Δ = 02-4·9·(-19)
Δ = 684
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{19}}{2*9}=\frac{0-6\sqrt{19}}{18} =-\frac{6\sqrt{19}}{18} =-\frac{\sqrt{19}}{3} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{19}}{2*9}=\frac{0+6\sqrt{19}}{18} =\frac{6\sqrt{19}}{18} =\frac{\sqrt{19}}{3} $
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