8p^2+6p-7=0

Solution for 8p^2+6p-7=0 equation:

Simplifying
8p2 + 6p + -7 = 0

Reorder the terms:
-7 + 6p + 8p2 = 0

Solving
-7 + 6p + 8p2 = 0

Solving for variable 'p'.

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

Divide each side by '8'.
-0.875 + 0.75p + p2 = 0

Move the constant term to the right:

Add '0.875' to each side of the equation.
-0.875 + 0.75p + 0.875 + p2 = 0 + 0.875

Reorder the terms:
-0.875 + 0.875 + 0.75p + p2 = 0 + 0.875

Combine like terms: -0.875 + 0.875 = 0.000
0.000 + 0.75p + p2 = 0 + 0.875
0.75p + p2 = 0 + 0.875

Combine like terms: 0 + 0.875 = 0.875
0.75p + p2 = 0.875

The p term is 0.75p.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75p + 0.140625 + p2 = 0.875 + 0.140625

Reorder the terms:
0.140625 + 0.75p + p2 = 0.875 + 0.140625

Combine like terms: 0.875 + 0.140625 = 1.015625
0.140625 + 0.75p + p2 = 1.015625

Factor a perfect square on the left side:
(p + 0.375)(p + 0.375) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(p + 0.375) equal to 1.007782219 and -1.007782219.

Subproblem 1
p + 0.375 = 1.007782219

Simplifying
p + 0.375 = 1.007782219

Reorder the terms:
0.375 + p = 1.007782219

Solving
0.375 + p = 1.007782219

Solving for variable 'p'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + p = 1.007782219 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + p = 1.007782219 + -0.375
p = 1.007782219 + -0.375

Combine like terms: 1.007782219 + -0.375 = 0.632782219
p = 0.632782219

Simplifying
p = 0.632782219

Subproblem 2
p + 0.375 = -1.007782219

Simplifying
p + 0.375 = -1.007782219

Reorder the terms:
0.375 + p = -1.007782219

Solving
0.375 + p = -1.007782219

Solving for variable 'p'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + p = -1.007782219 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + p = -1.007782219 + -0.375
p = -1.007782219 + -0.375

Combine like terms: -1.007782219 + -0.375 = -1.382782219
p = -1.382782219

Simplifying
p = -1.382782219

Solution
The solution to the problem is based on the solutions
from the subproblems.
p = {0.632782219, -1.382782219}