2z^2+5z+6=0

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

Simplifying
2z2 + 5z + 6 = 0

Reorder the terms:
6 + 5z + 2z2 = 0

Solving
6 + 5z + 2z2 = 0

Solving for variable 'z'.

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

Divide each side by '2'.
3 + 2.5z + z2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 2.5z + -3 + z2 = 0 + -3

Reorder the terms:
3 + -3 + 2.5z + z2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2.5z + z2 = 0 + -3
2.5z + z2 = 0 + -3

Combine like terms: 0 + -3 = -3
2.5z + z2 = -3

The z term is 2.5z.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5z + 1.5625 + z2 = -3 + 1.5625

Reorder the terms:
1.5625 + 2.5z + z2 = -3 + 1.5625

Combine like terms: -3 + 1.5625 = -1.4375
1.5625 + 2.5z + z2 = -1.4375

Factor a perfect square on the left side:
(z + 1.25)(z + 1.25) = -1.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.