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9n^2-22=-9n
We move all terms to the left:
9n^2-22-(-9n)=0
We get rid of parentheses
9n^2+9n-22=0
a = 9; b = 9; c = -22;
Δ = b2-4ac
Δ = 92-4·9·(-22)
Δ = 873
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{873}=\sqrt{9*97}=\sqrt{9}*\sqrt{97}=3\sqrt{97}$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{97}}{2*9}=\frac{-9-3\sqrt{97}}{18} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{97}}{2*9}=\frac{-9+3\sqrt{97}}{18} $
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