3x^2+4x-243=0

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Solution for 3x^2+4x-243=0 equation: 


Simplifying
3x2 + 4x + -243 = 0

Reorder the terms:
-243 + 4x + 3x2 = 0

Solving
-243 + 4x + 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'.
-81 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + 1.333333333x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + 1.333333333x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + 1.333333333x + x2 = 0 + 81
1.333333333x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
1.333333333x + x2 = 81

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 81 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 81 + 0.4444444442

Combine like terms: 81 + 0.4444444442 = 81.4444444442
0.4444444442 + 1.333333333x + x2 = 81.4444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 81.4444444442

Calculate the square root of the right side: 9.02465758

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 9.02465758 and -9.02465758.


Subproblem 1
x + 0.6666666665 = 9.02465758

Simplifying
x + 0.6666666665 = 9.02465758

Reorder the terms:
0.6666666665 + x = 9.02465758

Solving
0.6666666665 + x = 9.02465758

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = 9.02465758 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 9.02465758 + -0.6666666665
x = 9.02465758 + -0.6666666665

Combine like terms: 9.02465758 + -0.6666666665 = 8.3579909135
x = 8.3579909135

Simplifying
x = 8.3579909135


Subproblem 2
x + 0.6666666665 = -9.02465758

Simplifying
x + 0.6666666665 = -9.02465758

Reorder the terms:
0.6666666665 + x = -9.02465758

Solving
0.6666666665 + x = -9.02465758

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = -9.02465758 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -9.02465758 + -0.6666666665
x = -9.02465758 + -0.6666666665

Combine like terms: -9.02465758 + -0.6666666665 = -9.6913242465
x = -9.6913242465

Simplifying
x = -9.6913242465


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.3579909135, -9.6913242465}

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