-14=8x(6x-17)

Solution for -14=8x(6x-17) equation:

Simplifying
-14 = 8x(6x + -17)

Reorder the terms:
-14 = 8x(-17 + 6x)
-14 = (-17 * 8x + 6x * 8x)
-14 = (-136x + 48x2)

Solving
-14 = -136x + 48x2

Solving for variable 'x'.

Reorder the terms:
-14 + 136x + -48x2 = -136x + 136x + 48x2 + -48x2

Combine like terms: -136x + 136x = 0
-14 + 136x + -48x2 = 0 + 48x2 + -48x2
-14 + 136x + -48x2 = 48x2 + -48x2

Combine like terms: 48x2 + -48x2 = 0
-14 + 136x + -48x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 68x + -24x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + 68x + -24x2)' equal to zero and attempt to solve:

Simplifying
-7 + 68x + -24x2 = 0

Solving
-7 + 68x + -24x2 = 0

Begin completing the square.  Divide all terms by
-24 the coefficient of the squared term: 

Divide each side by '-24'.
0.2916666667 + -2.833333333x + x2 = 0

Move the constant term to the right:

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -2.833333333x + -0.2916666667 + x2 = 0 + -0.2916666667

Reorder the terms:
0.2916666667 + -0.2916666667 + -2.833333333x + x2 = 0 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + -2.833333333x + x2 = 0 + -0.2916666667
-2.833333333x + x2 = 0 + -0.2916666667

Combine like terms: 0 + -0.2916666667 = -0.2916666667
-2.833333333x + x2 = -0.2916666667

The x term is -2.833333333x.  Take half its coefficient (-1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
-2.833333333x + 2.006944445 + x2 = -0.2916666667 + 2.006944445

Reorder the terms:
2.006944445 + -2.833333333x + x2 = -0.2916666667 + 2.006944445

Combine like terms: -0.2916666667 + 2.006944445 = 1.7152777783
2.006944445 + -2.833333333x + x2 = 1.7152777783

Factor a perfect square on the left side:
(x + -1.416666667)(x + -1.416666667) = 1.7152777783

Calculate the square root of the right side: 1.309686137

Break this problem into two subproblems by setting 
(x + -1.416666667) equal to 1.309686137 and -1.309686137.

Subproblem 1
x + -1.416666667 = 1.309686137

Simplifying
x + -1.416666667 = 1.309686137

Reorder the terms:
-1.416666667 + x = 1.309686137

Solving
-1.416666667 + x = 1.309686137

Solving for variable 'x'.

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

Add '1.416666667' to each side of the equation.
-1.416666667 + 1.416666667 + x = 1.309686137 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + x = 1.309686137 + 1.416666667
x = 1.309686137 + 1.416666667

Combine like terms: 1.309686137 + 1.416666667 = 2.726352804
x = 2.726352804

Simplifying
x = 2.726352804

Subproblem 2
x + -1.416666667 = -1.309686137

Simplifying
x + -1.416666667 = -1.309686137

Reorder the terms:
-1.416666667 + x = -1.309686137

Solving
-1.416666667 + x = -1.309686137

Solving for variable 'x'.

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

Add '1.416666667' to each side of the equation.
-1.416666667 + 1.416666667 + x = -1.309686137 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + x = -1.309686137 + 1.416666667
x = -1.309686137 + 1.416666667

Combine like terms: -1.309686137 + 1.416666667 = 0.10698053
x = 0.10698053

Simplifying
x = 0.10698053

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.726352804, 0.10698053}
Solution
x = {2.726352804, 0.10698053}