3w^2-29w+20=0

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Solution for 3w^2-29w+20=0 equation: 


Simplifying
3w2 + -29w + 20 = 0

Reorder the terms:
20 + -29w + 3w2 = 0

Solving
20 + -29w + 3w2 = 0

Solving for variable 'w'.

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

Divide each side by '3'.
6.666666667 + -9.666666667w + w2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + -9.666666667w + -6.666666667 + w2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + -9.666666667w + w2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + -9.666666667w + w2 = 0 + -6.666666667
-9.666666667w + w2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
-9.666666667w + w2 = -6.666666667

The w term is -9.666666667w.  Take half its coefficient (-4.833333334).
Square it (23.36111112) and add it to both sides.

Add '23.36111112' to each side of the equation.
-9.666666667w + 23.36111112 + w2 = -6.666666667 + 23.36111112

Reorder the terms:
23.36111112 + -9.666666667w + w2 = -6.666666667 + 23.36111112

Combine like terms: -6.666666667 + 23.36111112 = 16.694444453
23.36111112 + -9.666666667w + w2 = 16.694444453

Factor a perfect square on the left side:
(w + -4.833333334)(w + -4.833333334) = 16.694444453

Calculate the square root of the right side: 4.085883558

Break this problem into two subproblems by setting 
(w + -4.833333334) equal to 4.085883558 and -4.085883558.


Subproblem 1
w + -4.833333334 = 4.085883558

Simplifying
w + -4.833333334 = 4.085883558

Reorder the terms:
-4.833333334 + w = 4.085883558

Solving
-4.833333334 + w = 4.085883558

Solving for variable 'w'.

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

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + w = 4.085883558 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + w = 4.085883558 + 4.833333334
w = 4.085883558 + 4.833333334

Combine like terms: 4.085883558 + 4.833333334 = 8.919216892
w = 8.919216892

Simplifying
w = 8.919216892


Subproblem 2
w + -4.833333334 = -4.085883558

Simplifying
w + -4.833333334 = -4.085883558

Reorder the terms:
-4.833333334 + w = -4.085883558

Solving
-4.833333334 + w = -4.085883558

Solving for variable 'w'.

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

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + w = -4.085883558 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + w = -4.085883558 + 4.833333334
w = -4.085883558 + 4.833333334

Combine like terms: -4.085883558 + 4.833333334 = 0.747449776
w = 0.747449776

Simplifying
w = 0.747449776


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {8.919216892, 0.747449776}

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