7z^2+14z+13=0

Solution for 7z^2+14z+13=0 equation:

Simplifying
7z2 + 14z + 13 = 0

Reorder the terms:
13 + 14z + 7z2 = 0

Solving
13 + 14z + 7z2 = 0

Solving for variable 'z'.

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

Divide each side by '7'.
1.857142857 + 2z + z2 = 0

Move the constant term to the right:

Add '-1.857142857' to each side of the equation.
1.857142857 + 2z + -1.857142857 + z2 = 0 + -1.857142857

Reorder the terms:
1.857142857 + -1.857142857 + 2z + z2 = 0 + -1.857142857

Combine like terms: 1.857142857 + -1.857142857 = 0.000000000
0.000000000 + 2z + z2 = 0 + -1.857142857
2z + z2 = 0 + -1.857142857

Combine like terms: 0 + -1.857142857 = -1.857142857
2z + z2 = -1.857142857

The z term is 2z.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2z + 1 + z2 = -1.857142857 + 1

Reorder the terms:
1 + 2z + z2 = -1.857142857 + 1

Combine like terms: -1.857142857 + 1 = -0.857142857
1 + 2z + z2 = -0.857142857

Factor a perfect square on the left side:
(z + 1)(z + 1) = -0.857142857

Can't calculate square root of the right side.

The solution to this equation could not be determined.