5x+6=9x^2-84x-196

Solution for 5x+6=9x^2-84x-196 equation:

Simplifying
5x + 6 = 9x2 + -84x + -196

Reorder the terms:
6 + 5x = 9x2 + -84x + -196

Reorder the terms:
6 + 5x = -196 + -84x + 9x2

Solving
6 + 5x = -196 + -84x + 9x2

Solving for variable 'x'.

Reorder the terms:
6 + 196 + 5x + 84x + -9x2 = -196 + -84x + 9x2 + 196 + 84x + -9x2

Combine like terms: 6 + 196 = 202
202 + 5x + 84x + -9x2 = -196 + -84x + 9x2 + 196 + 84x + -9x2

Combine like terms: 5x + 84x = 89x
202 + 89x + -9x2 = -196 + -84x + 9x2 + 196 + 84x + -9x2

Reorder the terms:
202 + 89x + -9x2 = -196 + 196 + -84x + 84x + 9x2 + -9x2

Combine like terms: -196 + 196 = 0
202 + 89x + -9x2 = 0 + -84x + 84x + 9x2 + -9x2
202 + 89x + -9x2 = -84x + 84x + 9x2 + -9x2

Combine like terms: -84x + 84x = 0
202 + 89x + -9x2 = 0 + 9x2 + -9x2
202 + 89x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
202 + 89x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-22.44444444 + -9.888888889x + x2 = 0

Move the constant term to the right:

Add '22.44444444' to each side of the equation.
-22.44444444 + -9.888888889x + 22.44444444 + x2 = 0 + 22.44444444

Reorder the terms:
-22.44444444 + 22.44444444 + -9.888888889x + x2 = 0 + 22.44444444

Combine like terms: -22.44444444 + 22.44444444 = 0.00000000
0.00000000 + -9.888888889x + x2 = 0 + 22.44444444
-9.888888889x + x2 = 0 + 22.44444444

Combine like terms: 0 + 22.44444444 = 22.44444444
-9.888888889x + x2 = 22.44444444

The x term is -9.888888889x.  Take half its coefficient (-4.944444445).
Square it (24.44753087) and add it to both sides.

Add '24.44753087' to each side of the equation.
-9.888888889x + 24.44753087 + x2 = 22.44444444 + 24.44753087

Reorder the terms:
24.44753087 + -9.888888889x + x2 = 22.44444444 + 24.44753087

Combine like terms: 22.44444444 + 24.44753087 = 46.89197531
24.44753087 + -9.888888889x + x2 = 46.89197531

Factor a perfect square on the left side:
(x + -4.944444445)(x + -4.944444445) = 46.89197531

Calculate the square root of the right side: 6.847771558

Break this problem into two subproblems by setting 
(x + -4.944444445) equal to 6.847771558 and -6.847771558.

Subproblem 1
x + -4.944444445 = 6.847771558

Simplifying
x + -4.944444445 = 6.847771558

Reorder the terms:
-4.944444445 + x = 6.847771558

Solving
-4.944444445 + x = 6.847771558

Solving for variable 'x'.

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

Add '4.944444445' to each side of the equation.
-4.944444445 + 4.944444445 + x = 6.847771558 + 4.944444445

Combine like terms: -4.944444445 + 4.944444445 = 0.000000000
0.000000000 + x = 6.847771558 + 4.944444445
x = 6.847771558 + 4.944444445

Combine like terms: 6.847771558 + 4.944444445 = 11.792216003
x = 11.792216003

Simplifying
x = 11.792216003

Subproblem 2
x + -4.944444445 = -6.847771558

Simplifying
x + -4.944444445 = -6.847771558

Reorder the terms:
-4.944444445 + x = -6.847771558

Solving
-4.944444445 + x = -6.847771558

Solving for variable 'x'.

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

Add '4.944444445' to each side of the equation.
-4.944444445 + 4.944444445 + x = -6.847771558 + 4.944444445

Combine like terms: -4.944444445 + 4.944444445 = 0.000000000
0.000000000 + x = -6.847771558 + 4.944444445
x = -6.847771558 + 4.944444445

Combine like terms: -6.847771558 + 4.944444445 = -1.903327113
x = -1.903327113

Simplifying
x = -1.903327113

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.792216003, -1.903327113}