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2+7n=2-9+5n(2)
We move all terms to the left:
2+7n-(2-9+5n(2))=0
We add all the numbers together, and all the variables
-(+5n^2+2-9)+7n+2=0
We get rid of parentheses
-5n^2+7n-2+9+2=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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