3w^2+13w-90=0

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Solution for 3w^2+13w-90=0 equation: 


Simplifying
3w2 + 13w + -90 = 0

Reorder the terms:
-90 + 13w + 3w2 = 0

Solving
-90 + 13w + 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'.
-30 + 4.333333333w + w2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 4.333333333w + 30 + w2 = 0 + 30

Reorder the terms:
-30 + 30 + 4.333333333w + w2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 4.333333333w + w2 = 0 + 30
4.333333333w + w2 = 0 + 30

Combine like terms: 0 + 30 = 30
4.333333333w + w2 = 30

The w term is 4.333333333w.  Take half its coefficient (2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
4.333333333w + 4.694444446 + w2 = 30 + 4.694444446

Reorder the terms:
4.694444446 + 4.333333333w + w2 = 30 + 4.694444446

Combine like terms: 30 + 4.694444446 = 34.694444446
4.694444446 + 4.333333333w + w2 = 34.694444446

Factor a perfect square on the left side:
(w + 2.166666667)(w + 2.166666667) = 34.694444446

Calculate the square root of the right side: 5.890199016

Break this problem into two subproblems by setting 
(w + 2.166666667) equal to 5.890199016 and -5.890199016.


Subproblem 1
w + 2.166666667 = 5.890199016

Simplifying
w + 2.166666667 = 5.890199016

Reorder the terms:
2.166666667 + w = 5.890199016

Solving
2.166666667 + w = 5.890199016

Solving for variable 'w'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + w = 5.890199016 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + w = 5.890199016 + -2.166666667
w = 5.890199016 + -2.166666667

Combine like terms: 5.890199016 + -2.166666667 = 3.723532349
w = 3.723532349

Simplifying
w = 3.723532349


Subproblem 2
w + 2.166666667 = -5.890199016

Simplifying
w + 2.166666667 = -5.890199016

Reorder the terms:
2.166666667 + w = -5.890199016

Solving
2.166666667 + w = -5.890199016

Solving for variable 'w'.

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

Add '-2.166666667' to each side of the equation.
2.166666667 + -2.166666667 + w = -5.890199016 + -2.166666667

Combine like terms: 2.166666667 + -2.166666667 = 0.000000000
0.000000000 + w = -5.890199016 + -2.166666667
w = -5.890199016 + -2.166666667

Combine like terms: -5.890199016 + -2.166666667 = -8.056865683
w = -8.056865683

Simplifying
w = -8.056865683


Solution
The solution to the problem is based on the solutions
from the subproblems.
w = {3.723532349, -8.056865683}

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