6x^2+19x-12=0

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Solution for 6x^2+19x-12=0 equation: 


Simplifying
6x2 + 19x + -12 = 0

Reorder the terms:
-12 + 19x + 6x2 = 0

Solving
-12 + 19x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-2 + 3.166666667x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 3.166666667x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 3.166666667x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 3.166666667x + x2 = 0 + 2
3.166666667x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
3.166666667x + x2 = 2

The x term is 3.166666667x.  Take half its coefficient (1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
3.166666667x + 2.506944447 + x2 = 2 + 2.506944447

Reorder the terms:
2.506944447 + 3.166666667x + x2 = 2 + 2.506944447

Combine like terms: 2 + 2.506944447 = 4.506944447
2.506944447 + 3.166666667x + x2 = 4.506944447

Factor a perfect square on the left side:
(x + 1.583333334)(x + 1.583333334) = 4.506944447

Calculate the square root of the right side: 2.122956534

Break this problem into two subproblems by setting 
(x + 1.583333334) equal to 2.122956534 and -2.122956534.


Subproblem 1
x + 1.583333334 = 2.122956534

Simplifying
x + 1.583333334 = 2.122956534

Reorder the terms:
1.583333334 + x = 2.122956534

Solving
1.583333334 + x = 2.122956534

Solving for variable 'x'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + x = 2.122956534 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + x = 2.122956534 + -1.583333334
x = 2.122956534 + -1.583333334

Combine like terms: 2.122956534 + -1.583333334 = 0.5396232
x = 0.5396232

Simplifying
x = 0.5396232


Subproblem 2
x + 1.583333334 = -2.122956534

Simplifying
x + 1.583333334 = -2.122956534

Reorder the terms:
1.583333334 + x = -2.122956534

Solving
1.583333334 + x = -2.122956534

Solving for variable 'x'.

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

Add '-1.583333334' to each side of the equation.
1.583333334 + -1.583333334 + x = -2.122956534 + -1.583333334

Combine like terms: 1.583333334 + -1.583333334 = 0.000000000
0.000000000 + x = -2.122956534 + -1.583333334
x = -2.122956534 + -1.583333334

Combine like terms: -2.122956534 + -1.583333334 = -3.706289868
x = -3.706289868

Simplifying
x = -3.706289868


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.5396232, -3.706289868}

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