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4n+1=5n(n+4)

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Solution for 4n+1=5n(n+4) equation:



4n+1=5n(n+4)
We move all terms to the left:
4n+1-(5n(n+4))=0
We calculate terms in parentheses: -(5n(n+4)), so:
5n(n+4)
We multiply parentheses
5n^2+20n
Back to the equation:
-(5n^2+20n)
We get rid of parentheses
-5n^2+4n-20n+1=0
We add all the numbers together, and all the variables
-5n^2-16n+1=0
a = -5; b = -16; c = +1;
Δ = b2-4ac
Δ = -162-4·(-5)·1
Δ = 276
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{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}
n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{69}}{2*-5}=\frac{16-2\sqrt{69}}{-10}
n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{69}}{2*-5}=\frac{16+2\sqrt{69}}{-10}

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