6a^2+5a+14=0

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Solution for 6a^2+5a+14=0 equation:


Simplifying
6a2 + 5a + 14 = 0

Reorder the terms:
14 + 5a + 6a2 = 0

Solving
14 + 5a + 6a2 = 0

Solving for variable 'a'.

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

Divide each side by '6'.
2.333333333 + 0.8333333333a + a2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + 0.8333333333a + -2.333333333 + a2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + 0.8333333333a + a2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + 0.8333333333a + a2 = 0 + -2.333333333
0.8333333333a + a2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
0.8333333333a + a2 = -2.333333333

The a term is 0.8333333333a.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333a + 0.1736111111 + a2 = -2.333333333 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333a + a2 = -2.333333333 + 0.1736111111

Combine like terms: -2.333333333 + 0.1736111111 = -2.1597222219
0.1736111111 + 0.8333333333a + a2 = -2.1597222219

Factor a perfect square on the left side:
(a + 0.4166666667)(a + 0.4166666667) = -2.1597222219

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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