7n^2+3n+6=0

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Solution for 7n^2+3n+6=0 equation:


Simplifying
7n2 + 3n + 6 = 0

Reorder the terms:
6 + 3n + 7n2 = 0

Solving
6 + 3n + 7n2 = 0

Solving for variable 'n'.

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

Divide each side by '7'.
0.8571428571 + 0.4285714286n + n2 = 0

Move the constant term to the right:

Add '-0.8571428571' to each side of the equation.
0.8571428571 + 0.4285714286n + -0.8571428571 + n2 = 0 + -0.8571428571

Reorder the terms:
0.8571428571 + -0.8571428571 + 0.4285714286n + n2 = 0 + -0.8571428571

Combine like terms: 0.8571428571 + -0.8571428571 = 0.0000000000
0.0000000000 + 0.4285714286n + n2 = 0 + -0.8571428571
0.4285714286n + n2 = 0 + -0.8571428571

Combine like terms: 0 + -0.8571428571 = -0.8571428571
0.4285714286n + n2 = -0.8571428571

The n term is 0.4285714286n.  Take half its coefficient (0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
0.4285714286n + 0.04591836735 + n2 = -0.8571428571 + 0.04591836735

Reorder the terms:
0.04591836735 + 0.4285714286n + n2 = -0.8571428571 + 0.04591836735

Combine like terms: -0.8571428571 + 0.04591836735 = -0.81122448975
0.04591836735 + 0.4285714286n + n2 = -0.81122448975

Factor a perfect square on the left side:
(n + 0.2142857143)(n + 0.2142857143) = -0.81122448975

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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