3x^2+3x+4=24

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Solution for 3x^2+3x+4=24 equation: 


Simplifying
3x2 + 3x + 4 = 24

Reorder the terms:
4 + 3x + 3x2 = 24

Solving
4 + 3x + 3x2 = 24

Solving for variable 'x'.

Reorder the terms:
4 + -24 + 3x + 3x2 = 24 + -24

Combine like terms: 4 + -24 = -20
-20 + 3x + 3x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-20 + 3x + 3x2 = 0

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

Divide each side by '3'.
-6.666666667 + x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + x + x2 = 0 + 6.666666667
x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
x + x2 = 6.666666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 6.666666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 6.666666667 + 0.25

Combine like terms: 6.666666667 + 0.25 = 6.916666667
1.25 + x2 = 6.916666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 6.916666667

Calculate the square root of the right side: 2.62995564

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.62995564 and -2.62995564.


Subproblem 1
x + 0.5 = 2.62995564

Simplifying
x + 0.5 = 2.62995564

Reorder the terms:
0.5 + x = 2.62995564

Solving
0.5 + x = 2.62995564

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 2.62995564 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 2.62995564 + -0.5
x = 2.62995564 + -0.5

Combine like terms: 2.62995564 + -0.5 = 2.12995564
x = 2.12995564

Simplifying
x = 2.12995564


Subproblem 2
x + 0.5 = -2.62995564

Simplifying
x + 0.5 = -2.62995564

Reorder the terms:
0.5 + x = -2.62995564

Solving
0.5 + x = -2.62995564

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -2.62995564 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -2.62995564 + -0.5
x = -2.62995564 + -0.5

Combine like terms: -2.62995564 + -0.5 = -3.12995564
x = -3.12995564

Simplifying
x = -3.12995564


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.12995564, -3.12995564}

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