3x^2+7=20x

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Solution for 3x^2+7=20x equation: 


Simplifying
3x2 + 7 = 20x

Reorder the terms:
7 + 3x2 = 20x

Solving
7 + 3x2 = 20x

Solving for variable 'x'.

Reorder the terms:
7 + -20x + 3x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
7 + -20x + 3x2 = 0

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

Divide each side by '3'.
2.333333333 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -6.666666667x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -6.666666667x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -6.666666667x + x2 = 0 + -2.333333333
-6.666666667x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-6.666666667x + x2 = -2.333333333

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = -2.333333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -2.333333333 + 11.11111112

Combine like terms: -2.333333333 + 11.11111112 = 8.777777787
11.11111112 + -6.666666667x + x2 = 8.777777787

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 8.777777787

Calculate the square root of the right side: 2.962731474

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 2.962731474 and -2.962731474.


Subproblem 1
x + -3.333333334 = 2.962731474

Simplifying
x + -3.333333334 = 2.962731474

Reorder the terms:
-3.333333334 + x = 2.962731474

Solving
-3.333333334 + x = 2.962731474

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 2.962731474 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 2.962731474 + 3.333333334
x = 2.962731474 + 3.333333334

Combine like terms: 2.962731474 + 3.333333334 = 6.296064808
x = 6.296064808

Simplifying
x = 6.296064808


Subproblem 2
x + -3.333333334 = -2.962731474

Simplifying
x + -3.333333334 = -2.962731474

Reorder the terms:
-3.333333334 + x = -2.962731474

Solving
-3.333333334 + x = -2.962731474

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -2.962731474 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -2.962731474 + 3.333333334
x = -2.962731474 + 3.333333334

Combine like terms: -2.962731474 + 3.333333334 = 0.37060186
x = 0.37060186

Simplifying
x = 0.37060186


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.296064808, 0.37060186}

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