8x^2+21x-12=0

Solution for 8x^2+21x-12=0 equation:

Simplifying
8x2 + 21x + -12 = 0

Reorder the terms:
-12 + 21x + 8x2 = 0

Solving
-12 + 21x + 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 + 2.625x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 2.625x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 2.625x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 2.625x + x2 = 0 + 1.5
2.625x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
2.625x + x2 = 1.5

The x term is 2.625x.  Take half its coefficient (1.3125).
Square it (1.72265625) and add it to both sides.

Add '1.72265625' to each side of the equation.
2.625x + 1.72265625 + x2 = 1.5 + 1.72265625

Reorder the terms:
1.72265625 + 2.625x + x2 = 1.5 + 1.72265625

Combine like terms: 1.5 + 1.72265625 = 3.22265625
1.72265625 + 2.625x + x2 = 3.22265625

Factor a perfect square on the left side:
(x + 1.3125)(x + 1.3125) = 3.22265625

Calculate the square root of the right side: 1.795175827

Break this problem into two subproblems by setting 
(x + 1.3125) equal to 1.795175827 and -1.795175827.

Subproblem 1
x + 1.3125 = 1.795175827

Simplifying
x + 1.3125 = 1.795175827

Reorder the terms:
1.3125 + x = 1.795175827

Solving
1.3125 + x = 1.795175827

Solving for variable 'x'.

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

Add '-1.3125' to each side of the equation.
1.3125 + -1.3125 + x = 1.795175827 + -1.3125

Combine like terms: 1.3125 + -1.3125 = 0.0000
0.0000 + x = 1.795175827 + -1.3125
x = 1.795175827 + -1.3125

Combine like terms: 1.795175827 + -1.3125 = 0.482675827
x = 0.482675827

Simplifying
x = 0.482675827

Subproblem 2
x + 1.3125 = -1.795175827

Simplifying
x + 1.3125 = -1.795175827

Reorder the terms:
1.3125 + x = -1.795175827

Solving
1.3125 + x = -1.795175827

Solving for variable 'x'.

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

Add '-1.3125' to each side of the equation.
1.3125 + -1.3125 + x = -1.795175827 + -1.3125

Combine like terms: 1.3125 + -1.3125 = 0.0000
0.0000 + x = -1.795175827 + -1.3125
x = -1.795175827 + -1.3125

Combine like terms: -1.795175827 + -1.3125 = -3.107675827
x = -3.107675827

Simplifying
x = -3.107675827

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.482675827, -3.107675827}