n/2(8n-4)=90

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Solution for n/2(8n-4)=90 equation: 


n in (-oo:+oo)

(n/2)*(8*n-4) = 90 // - 90

(n/2)*(8*n-4)-90 = 0

1/2*n*(8*n-4)-90 = 0

1/2*n*(8*n-4)-90 = 0

4*n^2-2*n-90 = 0

4*n^2-2*n-90 = 0

2*(2*n^2-n-45) = 0

2*n^2-n-45 = 0

DELTA = (-1)^2-(-45*2*4)

DELTA = 361

DELTA > 0

n = (361^(1/2)+1)/(2*2) or n = (1-361^(1/2))/(2*2)

n = 5 or n = -9/2

2*(n+9/2)*(n-5) = 0

2*(n+9/2)*(n-5) = 0

( 2 )

2 = 0

n belongs to the empty set

( n+9/2 )

n+9/2 = 0 // - 9/2

n = -9/2

( n-5 )

n-5 = 0 // + 5

n = 5

n in { -9/2, 5 }

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