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n(n-2)-1=5n-n-9
We move all terms to the left:
n(n-2)-1-(5n-n-9)=0
We add all the numbers together, and all the variables
n(n-2)-(4n-9)-1=0
We multiply parentheses
n^2-2n-(4n-9)-1=0
We get rid of parentheses
n^2-2n-4n+9-1=0
We add all the numbers together, and all the variables
n^2-6n+8=0
a = 1; b = -6; c = +8;
Δ = b2-4ac
Δ = -62-4·1·8
Δ = 4
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}$$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{4}=2$$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2}{2*1}=\frac{4}{2} =2 $$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2}{2*1}=\frac{8}{2} =4 $
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