3z^2+5z+6=0

Solution for 3z^2+5z+6=0 equation:

Simplifying
3z2 + 5z + 6 = 0

Reorder the terms:
6 + 5z + 3z2 = 0

Solving
6 + 5z + 3z2 = 0

Solving for variable 'z'.

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

Divide each side by '3'.
2 + 1.666666667z + z2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 1.666666667z + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + 1.666666667z + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 1.666666667z + z2 = 0 + -2
1.666666667z + z2 = 0 + -2

Combine like terms: 0 + -2 = -2
1.666666667z + z2 = -2

The z term is 1.666666667z.  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.
1.666666667z + 0.6944444447 + z2 = -2 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667z + z2 = -2 + 0.6944444447

Combine like terms: -2 + 0.6944444447 = -1.3055555553
0.6944444447 + 1.666666667z + z2 = -1.3055555553

Factor a perfect square on the left side:
(z + 0.8333333335)(z + 0.8333333335) = -1.3055555553

Can't calculate square root of the right side.

The solution to this equation could not be determined.