2z^2-z+6=0

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

Simplifying
2z2 + -1z + 6 = 0

Reorder the terms:
6 + -1z + 2z2 = 0

Solving
6 + -1z + 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 + -0.5z + z2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -0.5z + -3 + z2 = 0 + -3

Reorder the terms:
3 + -3 + -0.5z + z2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -0.5z + z2 = 0 + -3
-0.5z + z2 = 0 + -3

Combine like terms: 0 + -3 = -3
-0.5z + z2 = -3

The z term is -0.5z.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5z + 0.0625 + z2 = -3 + 0.0625

Reorder the terms:
0.0625 + -0.5z + z2 = -3 + 0.0625

Combine like terms: -3 + 0.0625 = -2.9375
0.0625 + -0.5z + z2 = -2.9375

Factor a perfect square on the left side:
(z + -0.25)(z + -0.25) = -2.9375

Can't calculate square root of the right side.

The solution to this equation could not be determined.