7n^2+6n+42=0

Solution for 7n^2+6n+42=0 equation:

Simplifying
7n2 + 6n + 42 = 0

Reorder the terms:
42 + 6n + 7n2 = 0

Solving
42 + 6n + 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'.
6 + 0.8571428571n + n2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 0.8571428571n + -6 + n2 = 0 + -6

Reorder the terms:
6 + -6 + 0.8571428571n + n2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 0.8571428571n + n2 = 0 + -6
0.8571428571n + n2 = 0 + -6

Combine like terms: 0 + -6 = -6
0.8571428571n + n2 = -6

The n term is 0.8571428571n.  Take half its coefficient (0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
0.8571428571n + 0.1836734694 + n2 = -6 + 0.1836734694

Reorder the terms:
0.1836734694 + 0.8571428571n + n2 = -6 + 0.1836734694

Combine like terms: -6 + 0.1836734694 = -5.8163265306
0.1836734694 + 0.8571428571n + n2 = -5.8163265306

Factor a perfect square on the left side:
(n + 0.4285714286)(n + 0.4285714286) = -5.8163265306

Can't calculate square root of the right side.

The solution to this equation could not be determined.