9x^2+4x=84

Solution for 9x^2+4x=84 equation:

Simplifying
9x2 + 4x = 84

Reorder the terms:
4x + 9x2 = 84

Solving
4x + 9x2 = 84

Solving for variable 'x'.

Reorder the terms:
-84 + 4x + 9x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + 4x + 9x2 = 0

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

Divide each side by '9'.
-9.333333333 + 0.4444444444x + x2 = 0

Move the constant term to the right:

Add '9.333333333' to each side of the equation.
-9.333333333 + 0.4444444444x + 9.333333333 + x2 = 0 + 9.333333333

Reorder the terms:
-9.333333333 + 9.333333333 + 0.4444444444x + x2 = 0 + 9.333333333

Combine like terms: -9.333333333 + 9.333333333 = 0.000000000
0.000000000 + 0.4444444444x + x2 = 0 + 9.333333333
0.4444444444x + x2 = 0 + 9.333333333

Combine like terms: 0 + 9.333333333 = 9.333333333
0.4444444444x + x2 = 9.333333333

The x term is 0.4444444444x.  Take half its coefficient (0.2222222222).
Square it (0.04938271604) and add it to both sides.

Add '0.04938271604' to each side of the equation.
0.4444444444x + 0.04938271604 + x2 = 9.333333333 + 0.04938271604

Reorder the terms:
0.04938271604 + 0.4444444444x + x2 = 9.333333333 + 0.04938271604

Combine like terms: 9.333333333 + 0.04938271604 = 9.38271604904
0.04938271604 + 0.4444444444x + x2 = 9.38271604904

Factor a perfect square on the left side:
(x + 0.2222222222)(x + 0.2222222222) = 9.38271604904

Calculate the square root of the right side: 3.063121945

Break this problem into two subproblems by setting 
(x + 0.2222222222) equal to 3.063121945 and -3.063121945.

Subproblem 1
x + 0.2222222222 = 3.063121945

Simplifying
x + 0.2222222222 = 3.063121945

Reorder the terms:
0.2222222222 + x = 3.063121945

Solving
0.2222222222 + x = 3.063121945

Solving for variable 'x'.

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

Add '-0.2222222222' to each side of the equation.
0.2222222222 + -0.2222222222 + x = 3.063121945 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + x = 3.063121945 + -0.2222222222
x = 3.063121945 + -0.2222222222

Combine like terms: 3.063121945 + -0.2222222222 = 2.8408997228
x = 2.8408997228

Simplifying
x = 2.8408997228

Subproblem 2
x + 0.2222222222 = -3.063121945

Simplifying
x + 0.2222222222 = -3.063121945

Reorder the terms:
0.2222222222 + x = -3.063121945

Solving
0.2222222222 + x = -3.063121945

Solving for variable 'x'.

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

Add '-0.2222222222' to each side of the equation.
0.2222222222 + -0.2222222222 + x = -3.063121945 + -0.2222222222

Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000
0.0000000000 + x = -3.063121945 + -0.2222222222
x = -3.063121945 + -0.2222222222

Combine like terms: -3.063121945 + -0.2222222222 = -3.2853441672
x = -3.2853441672

Simplifying
x = -3.2853441672

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.8408997228, -3.2853441672}