8x^2+17x-12=0

Solution for 8x^2+17x-12=0 equation:

Simplifying
8x2 + 17x + -12 = 0

Reorder the terms:
-12 + 17x + 8x2 = 0

Solving
-12 + 17x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-1.5 + 2.125x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 2.125x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 2.125x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 2.125x + x2 = 0 + 1.5
2.125x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
2.125x + x2 = 1.5

The x term is 2.125x.  Take half its coefficient (1.0625).
Square it (1.12890625) and add it to both sides.

Add '1.12890625' to each side of the equation.
2.125x + 1.12890625 + x2 = 1.5 + 1.12890625

Reorder the terms:
1.12890625 + 2.125x + x2 = 1.5 + 1.12890625

Combine like terms: 1.5 + 1.12890625 = 2.62890625
1.12890625 + 2.125x + x2 = 2.62890625

Factor a perfect square on the left side:
(x + 1.0625)(x + 1.0625) = 2.62890625

Calculate the square root of the right side: 1.621390221

Break this problem into two subproblems by setting 
(x + 1.0625) equal to 1.621390221 and -1.621390221.

Subproblem 1
x + 1.0625 = 1.621390221

Simplifying
x + 1.0625 = 1.621390221

Reorder the terms:
1.0625 + x = 1.621390221

Solving
1.0625 + x = 1.621390221

Solving for variable 'x'.

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

Add '-1.0625' to each side of the equation.
1.0625 + -1.0625 + x = 1.621390221 + -1.0625

Combine like terms: 1.0625 + -1.0625 = 0.0000
0.0000 + x = 1.621390221 + -1.0625
x = 1.621390221 + -1.0625

Combine like terms: 1.621390221 + -1.0625 = 0.558890221
x = 0.558890221

Simplifying
x = 0.558890221

Subproblem 2
x + 1.0625 = -1.621390221

Simplifying
x + 1.0625 = -1.621390221

Reorder the terms:
1.0625 + x = -1.621390221

Solving
1.0625 + x = -1.621390221

Solving for variable 'x'.

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

Add '-1.0625' to each side of the equation.
1.0625 + -1.0625 + x = -1.621390221 + -1.0625

Combine like terms: 1.0625 + -1.0625 = 0.0000
0.0000 + x = -1.621390221 + -1.0625
x = -1.621390221 + -1.0625

Combine like terms: -1.621390221 + -1.0625 = -2.683890221
x = -2.683890221

Simplifying
x = -2.683890221

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.558890221, -2.683890221}