3x^2-5x-99=0

Solution for 3x^2-5x-99=0 equation:

Simplifying
3x2 + -5x + -99 = 0

Reorder the terms:
-99 + -5x + 3x2 = 0

Solving
-99 + -5x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-33 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -1.666666667x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + -1.666666667x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -1.666666667x + x2 = 0 + 33
-1.666666667x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
-1.666666667x + x2 = 33

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 33 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 33 + 0.6944444447

Combine like terms: 33 + 0.6944444447 = 33.6944444447
0.6944444447 + -1.666666667x + x2 = 33.6944444447

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 33.6944444447

Calculate the square root of the right side: 5.804691589

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 5.804691589 and -5.804691589.

Subproblem 1
x + -0.8333333335 = 5.804691589

Simplifying
x + -0.8333333335 = 5.804691589

Reorder the terms:
-0.8333333335 + x = 5.804691589

Solving
-0.8333333335 + x = 5.804691589

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 5.804691589 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 5.804691589 + 0.8333333335
x = 5.804691589 + 0.8333333335

Combine like terms: 5.804691589 + 0.8333333335 = 6.6380249225
x = 6.6380249225

Simplifying
x = 6.6380249225

Subproblem 2
x + -0.8333333335 = -5.804691589

Simplifying
x + -0.8333333335 = -5.804691589

Reorder the terms:
-0.8333333335 + x = -5.804691589

Solving
-0.8333333335 + x = -5.804691589

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -5.804691589 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -5.804691589 + 0.8333333335
x = -5.804691589 + 0.8333333335

Combine like terms: -5.804691589 + 0.8333333335 = -4.9713582555
x = -4.9713582555

Simplifying
x = -4.9713582555

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.6380249225, -4.9713582555}