3x^2-20x=130

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Solution for 3x^2-20x=130 equation: 


Simplifying
3x2 + -20x = 130

Reorder the terms:
-20x + 3x2 = 130

Solving
-20x + 3x2 = 130

Solving for variable 'x'.

Reorder the terms:
-130 + -20x + 3x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-130 + -20x + 3x2 = 0

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

Divide each side by '3'.
-43.33333333 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '43.33333333' to each side of the equation.
-43.33333333 + -6.666666667x + 43.33333333 + x2 = 0 + 43.33333333

Reorder the terms:
-43.33333333 + 43.33333333 + -6.666666667x + x2 = 0 + 43.33333333

Combine like terms: -43.33333333 + 43.33333333 = 0.00000000
0.00000000 + -6.666666667x + x2 = 0 + 43.33333333
-6.666666667x + x2 = 0 + 43.33333333

Combine like terms: 0 + 43.33333333 = 43.33333333
-6.666666667x + x2 = 43.33333333

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 = 43.33333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = 43.33333333 + 11.11111112

Combine like terms: 43.33333333 + 11.11111112 = 54.44444445
11.11111112 + -6.666666667x + x2 = 54.44444445

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 54.44444445

Calculate the square root of the right side: 7.378647874

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 7.378647874 and -7.378647874.


Subproblem 1
x + -3.333333334 = 7.378647874

Simplifying
x + -3.333333334 = 7.378647874

Reorder the terms:
-3.333333334 + x = 7.378647874

Solving
-3.333333334 + x = 7.378647874

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 = 7.378647874 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 7.378647874 + 3.333333334
x = 7.378647874 + 3.333333334

Combine like terms: 7.378647874 + 3.333333334 = 10.711981208
x = 10.711981208

Simplifying
x = 10.711981208


Subproblem 2
x + -3.333333334 = -7.378647874

Simplifying
x + -3.333333334 = -7.378647874

Reorder the terms:
-3.333333334 + x = -7.378647874

Solving
-3.333333334 + x = -7.378647874

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 = -7.378647874 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -7.378647874 + 3.333333334
x = -7.378647874 + 3.333333334

Combine like terms: -7.378647874 + 3.333333334 = -4.04531454
x = -4.04531454

Simplifying
x = -4.04531454


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.711981208, -4.04531454}

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