3x^2-20x+30=0

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Solution for 3x^2-20x+30=0 equation: 


Simplifying
3x2 + -20x + 30 = 0

Reorder the terms:
30 + -20x + 3x2 = 0

Solving
30 + -20x + 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'.
10 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -6.666666667x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -6.666666667x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -6.666666667x + x2 = 0 + -10
-6.666666667x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-6.666666667x + x2 = -10

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 = -10 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = -10 + 11.11111112

Combine like terms: -10 + 11.11111112 = 1.11111112
11.11111112 + -6.666666667x + x2 = 1.11111112

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 1.11111112

Calculate the square root of the right side: 1.054092558

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 1.054092558 and -1.054092558.


Subproblem 1
x + -3.333333334 = 1.054092558

Simplifying
x + -3.333333334 = 1.054092558

Reorder the terms:
-3.333333334 + x = 1.054092558

Solving
-3.333333334 + x = 1.054092558

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 = 1.054092558 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 1.054092558 + 3.333333334
x = 1.054092558 + 3.333333334

Combine like terms: 1.054092558 + 3.333333334 = 4.387425892
x = 4.387425892

Simplifying
x = 4.387425892


Subproblem 2
x + -3.333333334 = -1.054092558

Simplifying
x + -3.333333334 = -1.054092558

Reorder the terms:
-3.333333334 + x = -1.054092558

Solving
-3.333333334 + x = -1.054092558

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 = -1.054092558 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -1.054092558 + 3.333333334
x = -1.054092558 + 3.333333334

Combine like terms: -1.054092558 + 3.333333334 = 2.279240776
x = 2.279240776

Simplifying
x = 2.279240776


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.387425892, 2.279240776}

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