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0=n^2+19n-84
We move all terms to the left:
0-(n^2+19n-84)=0
We add all the numbers together, and all the variables
-(n^2+19n-84)=0
We get rid of parentheses
-n^2-19n+84=0
We add all the numbers together, and all the variables
-1n^2-19n+84=0
a = -1; b = -19; c = +84;
Δ = b2-4ac
Δ = -192-4·(-1)·84
Δ = 697
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{-(-19)-\sqrt{697}}{2*-1}=\frac{19-\sqrt{697}}{-2} $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{697}}{2*-1}=\frac{19+\sqrt{697}}{-2} $
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