6a^2+35a+123=0

Solution for 6a^2+35a+123=0 equation:

Simplifying
6a2 + 35a + 123 = 0

Reorder the terms:
123 + 35a + 6a2 = 0

Solving
123 + 35a + 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'.
20.5 + 5.833333333a + a2 = 0

Move the constant term to the right:

Add '-20.5' to each side of the equation.
20.5 + 5.833333333a + -20.5 + a2 = 0 + -20.5

Reorder the terms:
20.5 + -20.5 + 5.833333333a + a2 = 0 + -20.5

Combine like terms: 20.5 + -20.5 = 0.0
0.0 + 5.833333333a + a2 = 0 + -20.5
5.833333333a + a2 = 0 + -20.5

Combine like terms: 0 + -20.5 = -20.5
5.833333333a + a2 = -20.5

The a term is 5.833333333a.  Take half its coefficient (2.916666667).
Square it (8.506944446) and add it to both sides.

Add '8.506944446' to each side of the equation.
5.833333333a + 8.506944446 + a2 = -20.5 + 8.506944446

Reorder the terms:
8.506944446 + 5.833333333a + a2 = -20.5 + 8.506944446

Combine like terms: -20.5 + 8.506944446 = -11.993055554
8.506944446 + 5.833333333a + a2 = -11.993055554

Factor a perfect square on the left side:
(a + 2.916666667)(a + 2.916666667) = -11.993055554

Can't calculate square root of the right side.

The solution to this equation could not be determined.