5z^2+4z+8=0

Solution for 5z^2+4z+8=0 equation:

Simplifying
5z2 + 4z + 8 = 0

Reorder the terms:
8 + 4z + 5z2 = 0

Solving
8 + 4z + 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'.
1.6 + 0.8z + z2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + 0.8z + -1.6 + z2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + 0.8z + z2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + 0.8z + z2 = 0 + -1.6
0.8z + z2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
0.8z + z2 = -1.6

The z term is 0.8z.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8z + 0.16 + z2 = -1.6 + 0.16

Reorder the terms:
0.16 + 0.8z + z2 = -1.6 + 0.16

Combine like terms: -1.6 + 0.16 = -1.44
0.16 + 0.8z + z2 = -1.44

Factor a perfect square on the left side:
(z + 0.4)(z + 0.4) = -1.44

Can't calculate square root of the right side.

The solution to this equation could not be determined.