3n^2+5n=-11

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Solution for 3n^2+5n=-11 equation: 


Simplifying
3n2 + 5n = -11

Reorder the terms:
5n + 3n2 = -11

Solving
5n + 3n2 = -11

Solving for variable 'n'.

Reorder the terms:
11 + 5n + 3n2 = -11 + 11

Combine like terms: -11 + 11 = 0
11 + 5n + 3n2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
3.666666667 + 1.666666667n + n2 = 0

Move the constant term to the right:

Add '-3.666666667' to each side of the equation.
3.666666667 + 1.666666667n + -3.666666667 + n2 = 0 + -3.666666667

Reorder the terms:
3.666666667 + -3.666666667 + 1.666666667n + n2 = 0 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + 1.666666667n + n2 = 0 + -3.666666667
1.666666667n + n2 = 0 + -3.666666667

Combine like terms: 0 + -3.666666667 = -3.666666667
1.666666667n + n2 = -3.666666667

The n term is 1.666666667n.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667n + 0.6944444447 + n2 = -3.666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667n + n2 = -3.666666667 + 0.6944444447

Combine like terms: -3.666666667 + 0.6944444447 = -2.9722222223
0.6944444447 + 1.666666667n + n2 = -2.9722222223

Factor a perfect square on the left side:
(n + 0.8333333335)(n + 0.8333333335) = -2.9722222223

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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