5z^2+6z-7=0

Solution for 5z^2+6z-7=0 equation:

Simplifying
5z2 + 6z + -7 = 0

Reorder the terms:
-7 + 6z + 5z2 = 0

Solving
-7 + 6z + 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'.
-1.4 + 1.2z + z2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + 1.2z + 1.4 + z2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + 1.2z + z2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + 1.2z + z2 = 0 + 1.4
1.2z + z2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
1.2z + z2 = 1.4

The z term is 1.2z.  Take half its coefficient (0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
1.2z + 0.36 + z2 = 1.4 + 0.36

Reorder the terms:
0.36 + 1.2z + z2 = 1.4 + 0.36

Combine like terms: 1.4 + 0.36 = 1.76
0.36 + 1.2z + z2 = 1.76

Factor a perfect square on the left side:
(z + 0.6)(z + 0.6) = 1.76

Calculate the square root of the right side: 1.326649916

Break this problem into two subproblems by setting 
(z + 0.6) equal to 1.326649916 and -1.326649916.

Subproblem 1
z + 0.6 = 1.326649916

Simplifying
z + 0.6 = 1.326649916

Reorder the terms:
0.6 + z = 1.326649916

Solving
0.6 + z = 1.326649916

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '-0.6' to each side of the equation.
0.6 + -0.6 + z = 1.326649916 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + z = 1.326649916 + -0.6
z = 1.326649916 + -0.6

Combine like terms: 1.326649916 + -0.6 = 0.726649916
z = 0.726649916

Simplifying
z = 0.726649916

Subproblem 2
z + 0.6 = -1.326649916

Simplifying
z + 0.6 = -1.326649916

Reorder the terms:
0.6 + z = -1.326649916

Solving
0.6 + z = -1.326649916

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '-0.6' to each side of the equation.
0.6 + -0.6 + z = -1.326649916 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + z = -1.326649916 + -0.6
z = -1.326649916 + -0.6

Combine like terms: -1.326649916 + -0.6 = -1.926649916
z = -1.926649916

Simplifying
z = -1.926649916

Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.726649916, -1.926649916}