306=n/2(2*9+3n*3)

Solution for 306=n/2(2*9+3n*3) equation:

n in (-oo:+oo)

306 = (n/2)*(3*3*n+2*9) // - (n/2)*(3*3*n+2*9)

306-((n/2)*(3*3*n+2*9)) = 0

306-1*1/2*n*(9*n+18) = 0

306-1*1/2*n*(9*n+18) = 0

306-9/2*n^2-9*n = 0

306-9/2*n^2-9*n = 0

9*(34-1/2*n^2-n) = 0

34-1/2*n^2-n = 0

DELTA = (-1)^2-(-1/2*4*34)

DELTA = 69

DELTA > 0

n = (69^(1/2)+1)/(-1/2*2) or n = (1-69^(1/2))/(-1/2*2)

n = -(69^(1/2)+1) or n = 69^(1/2)-1

9*(n+69^(1/2)+1)*(n-69^(1/2)+1) = 0

9*(n+69^(1/2)+1)*(n-69^(1/2)+1) = 0

( n+69^(1/2)+1 )

n+69^(1/2)+1 = 0 // - 69^(1/2)+1

n = -(69^(1/2)+1)

( n-69^(1/2)+1 )

n-69^(1/2)+1 = 0 // - 1-69^(1/2)

n = -(1-69^(1/2))

n = 69^(1/2)-1

n in { -(69^(1/2)+1), 69^(1/2)-1 }