3x^2+2x=76

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Solution for 3x^2+2x=76 equation: 


Simplifying
3x2 + 2x = 76

Reorder the terms:
2x + 3x2 = 76

Solving
2x + 3x2 = 76

Solving for variable 'x'.

Reorder the terms:
-76 + 2x + 3x2 = 76 + -76

Combine like terms: 76 + -76 = 0
-76 + 2x + 3x2 = 0

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

Divide each side by '3'.
-25.33333333 + 0.6666666667x + x2 = 0

Move the constant term to the right:

Add '25.33333333' to each side of the equation.
-25.33333333 + 0.6666666667x + 25.33333333 + x2 = 0 + 25.33333333

Reorder the terms:
-25.33333333 + 25.33333333 + 0.6666666667x + x2 = 0 + 25.33333333

Combine like terms: -25.33333333 + 25.33333333 = 0.00000000
0.00000000 + 0.6666666667x + x2 = 0 + 25.33333333
0.6666666667x + x2 = 0 + 25.33333333

Combine like terms: 0 + 25.33333333 = 25.33333333
0.6666666667x + x2 = 25.33333333

The x term is 0.6666666667x.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667x + 0.1111111112 + x2 = 25.33333333 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667x + x2 = 25.33333333 + 0.1111111112

Combine like terms: 25.33333333 + 0.1111111112 = 25.4444444412
0.1111111112 + 0.6666666667x + x2 = 25.4444444412

Factor a perfect square on the left side:
(x + 0.3333333334)(x + 0.3333333334) = 25.4444444412

Calculate the square root of the right side: 5.04424865

Break this problem into two subproblems by setting 
(x + 0.3333333334) equal to 5.04424865 and -5.04424865.


Subproblem 1
x + 0.3333333334 = 5.04424865

Simplifying
x + 0.3333333334 = 5.04424865

Reorder the terms:
0.3333333334 + x = 5.04424865

Solving
0.3333333334 + x = 5.04424865

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = 5.04424865 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = 5.04424865 + -0.3333333334
x = 5.04424865 + -0.3333333334

Combine like terms: 5.04424865 + -0.3333333334 = 4.7109153166
x = 4.7109153166

Simplifying
x = 4.7109153166


Subproblem 2
x + 0.3333333334 = -5.04424865

Simplifying
x + 0.3333333334 = -5.04424865

Reorder the terms:
0.3333333334 + x = -5.04424865

Solving
0.3333333334 + x = -5.04424865

Solving for variable 'x'.

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

Add '-0.3333333334' to each side of the equation.
0.3333333334 + -0.3333333334 + x = -5.04424865 + -0.3333333334

Combine like terms: 0.3333333334 + -0.3333333334 = 0.0000000000
0.0000000000 + x = -5.04424865 + -0.3333333334
x = -5.04424865 + -0.3333333334

Combine like terms: -5.04424865 + -0.3333333334 = -5.3775819834
x = -5.3775819834

Simplifying
x = -5.3775819834


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.7109153166, -5.3775819834}

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