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2n+5n^2-9=9n
We move all terms to the left:
2n+5n^2-9-(9n)=0
We add all the numbers together, and all the variables
5n^2-7n-9=0
a = 5; b = -7; c = -9;
Δ = b2-4ac
Δ = -72-4·5·(-9)
Δ = 229
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{-(-7)-\sqrt{229}}{2*5}=\frac{7-\sqrt{229}}{10} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{229}}{2*5}=\frac{7+\sqrt{229}}{10} $
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