3x^2-50x+105=0

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Solution for 3x^2-50x+105=0 equation: 


Simplifying
3x2 + -50x + 105 = 0

Reorder the terms:
105 + -50x + 3x2 = 0

Solving
105 + -50x + 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'.
35 + -16.66666667x + x2 = 0

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + -16.66666667x + -35 + x2 = 0 + -35

Reorder the terms:
35 + -35 + -16.66666667x + x2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -16.66666667x + x2 = 0 + -35
-16.66666667x + x2 = 0 + -35

Combine like terms: 0 + -35 = -35
-16.66666667x + x2 = -35

The x term is -16.66666667x.  Take half its coefficient (-8.333333335).
Square it (69.44444447) and add it to both sides.

Add '69.44444447' to each side of the equation.
-16.66666667x + 69.44444447 + x2 = -35 + 69.44444447

Reorder the terms:
69.44444447 + -16.66666667x + x2 = -35 + 69.44444447

Combine like terms: -35 + 69.44444447 = 34.44444447
69.44444447 + -16.66666667x + x2 = 34.44444447

Factor a perfect square on the left side:
(x + -8.333333335)(x + -8.333333335) = 34.44444447

Calculate the square root of the right side: 5.868938956

Break this problem into two subproblems by setting 
(x + -8.333333335) equal to 5.868938956 and -5.868938956.


Subproblem 1
x + -8.333333335 = 5.868938956

Simplifying
x + -8.333333335 = 5.868938956

Reorder the terms:
-8.333333335 + x = 5.868938956

Solving
-8.333333335 + x = 5.868938956

Solving for variable 'x'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + x = 5.868938956 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = 5.868938956 + 8.333333335
x = 5.868938956 + 8.333333335

Combine like terms: 5.868938956 + 8.333333335 = 14.202272291
x = 14.202272291

Simplifying
x = 14.202272291


Subproblem 2
x + -8.333333335 = -5.868938956

Simplifying
x + -8.333333335 = -5.868938956

Reorder the terms:
-8.333333335 + x = -5.868938956

Solving
-8.333333335 + x = -5.868938956

Solving for variable 'x'.

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

Add '8.333333335' to each side of the equation.
-8.333333335 + 8.333333335 + x = -5.868938956 + 8.333333335

Combine like terms: -8.333333335 + 8.333333335 = 0.000000000
0.000000000 + x = -5.868938956 + 8.333333335
x = -5.868938956 + 8.333333335

Combine like terms: -5.868938956 + 8.333333335 = 2.464394379
x = 2.464394379

Simplifying
x = 2.464394379


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.202272291, 2.464394379}

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