5z^2+8z+6=0

Solution for 5z^2+8z+6=0 equation:

Simplifying
5z2 + 8z + 6 = 0

Reorder the terms:
6 + 8z + 5z2 = 0

Solving
6 + 8z + 5z2 = 0

Solving for variable 'z'.

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

Divide each side by '5'.
1.2 + 1.6z + z2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 1.6z + -1.2 + z2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 1.6z + z2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 1.6z + z2 = 0 + -1.2
1.6z + z2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
1.6z + z2 = -1.2

The z term is 1.6z.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6z + 0.64 + z2 = -1.2 + 0.64

Reorder the terms:
0.64 + 1.6z + z2 = -1.2 + 0.64

Combine like terms: -1.2 + 0.64 = -0.56
0.64 + 1.6z + z2 = -0.56

Factor a perfect square on the left side:
(z + 0.8)(z + 0.8) = -0.56

Can't calculate square root of the right side.

The solution to this equation could not be determined.