12x^2+19x-76=0

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Solution for 12x^2+19x-76=0 equation: 


Simplifying
12x2 + 19x + -76 = 0

Reorder the terms:
-76 + 19x + 12x2 = 0

Solving
-76 + 19x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
-6.333333333 + 1.583333333x + x2 = 0

Move the constant term to the right:

Add '6.333333333' to each side of the equation.
-6.333333333 + 1.583333333x + 6.333333333 + x2 = 0 + 6.333333333

Reorder the terms:
-6.333333333 + 6.333333333 + 1.583333333x + x2 = 0 + 6.333333333

Combine like terms: -6.333333333 + 6.333333333 = 0.000000000
0.000000000 + 1.583333333x + x2 = 0 + 6.333333333
1.583333333x + x2 = 0 + 6.333333333

Combine like terms: 0 + 6.333333333 = 6.333333333
1.583333333x + x2 = 6.333333333

The x term is 1.583333333x.  Take half its coefficient (0.7916666665).
Square it (0.6267361108) and add it to both sides.

Add '0.6267361108' to each side of the equation.
1.583333333x + 0.6267361108 + x2 = 6.333333333 + 0.6267361108

Reorder the terms:
0.6267361108 + 1.583333333x + x2 = 6.333333333 + 0.6267361108

Combine like terms: 6.333333333 + 0.6267361108 = 6.9600694438
0.6267361108 + 1.583333333x + x2 = 6.9600694438

Factor a perfect square on the left side:
(x + 0.7916666665)(x + 0.7916666665) = 6.9600694438

Calculate the square root of the right side: 2.638194353

Break this problem into two subproblems by setting 
(x + 0.7916666665) equal to 2.638194353 and -2.638194353.


Subproblem 1
x + 0.7916666665 = 2.638194353

Simplifying
x + 0.7916666665 = 2.638194353

Reorder the terms:
0.7916666665 + x = 2.638194353

Solving
0.7916666665 + x = 2.638194353

Solving for variable 'x'.

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

Add '-0.7916666665' to each side of the equation.
0.7916666665 + -0.7916666665 + x = 2.638194353 + -0.7916666665

Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000
0.0000000000 + x = 2.638194353 + -0.7916666665
x = 2.638194353 + -0.7916666665

Combine like terms: 2.638194353 + -0.7916666665 = 1.8465276865
x = 1.8465276865

Simplifying
x = 1.8465276865


Subproblem 2
x + 0.7916666665 = -2.638194353

Simplifying
x + 0.7916666665 = -2.638194353

Reorder the terms:
0.7916666665 + x = -2.638194353

Solving
0.7916666665 + x = -2.638194353

Solving for variable 'x'.

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

Add '-0.7916666665' to each side of the equation.
0.7916666665 + -0.7916666665 + x = -2.638194353 + -0.7916666665

Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000
0.0000000000 + x = -2.638194353 + -0.7916666665
x = -2.638194353 + -0.7916666665

Combine like terms: -2.638194353 + -0.7916666665 = -3.4298610195
x = -3.4298610195

Simplifying
x = -3.4298610195


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.8465276865, -3.4298610195}

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