2x^2+21x-12=0

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

Simplifying
2x2 + 21x + -12 = 0

Reorder the terms:
-12 + 21x + 2x2 = 0

Solving
-12 + 21x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-6 + 10.5x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 10.5x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + 10.5x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 10.5x + x2 = 0 + 6
10.5x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
10.5x + x2 = 6

The x term is 10.5x.  Take half its coefficient (5.25).
Square it (27.5625) and add it to both sides.

Add '27.5625' to each side of the equation.
10.5x + 27.5625 + x2 = 6 + 27.5625

Reorder the terms:
27.5625 + 10.5x + x2 = 6 + 27.5625

Combine like terms: 6 + 27.5625 = 33.5625
27.5625 + 10.5x + x2 = 33.5625

Factor a perfect square on the left side:
(x + 5.25)(x + 5.25) = 33.5625

Calculate the square root of the right side: 5.793315113

Break this problem into two subproblems by setting 
(x + 5.25) equal to 5.793315113 and -5.793315113.

Subproblem 1
x + 5.25 = 5.793315113

Simplifying
x + 5.25 = 5.793315113

Reorder the terms:
5.25 + x = 5.793315113

Solving
5.25 + x = 5.793315113

Solving for variable 'x'.

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

Add '-5.25' to each side of the equation.
5.25 + -5.25 + x = 5.793315113 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + x = 5.793315113 + -5.25
x = 5.793315113 + -5.25

Combine like terms: 5.793315113 + -5.25 = 0.543315113
x = 0.543315113

Simplifying
x = 0.543315113

Subproblem 2
x + 5.25 = -5.793315113

Simplifying
x + 5.25 = -5.793315113

Reorder the terms:
5.25 + x = -5.793315113

Solving
5.25 + x = -5.793315113

Solving for variable 'x'.

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

Add '-5.25' to each side of the equation.
5.25 + -5.25 + x = -5.793315113 + -5.25

Combine like terms: 5.25 + -5.25 = 0.00
0.00 + x = -5.793315113 + -5.25
x = -5.793315113 + -5.25

Combine like terms: -5.793315113 + -5.25 = -11.043315113
x = -11.043315113

Simplifying
x = -11.043315113

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.543315113, -11.043315113}