3x^2+x-20000=0

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Solution for 3x^2+x-20000=0 equation:


Simplifying
3x2 + x + -20000 = 0

Reorder the terms:
-20000 + x + 3x2 = 0

Solving
-20000 + x + 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'.
-6666.666667 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '6666.666667' to each side of the equation.
-6666.666667 + 0.3333333333x + 6666.666667 + x2 = 0 + 6666.666667

Reorder the terms:
-6666.666667 + 6666.666667 + 0.3333333333x + x2 = 0 + 6666.666667

Combine like terms: -6666.666667 + 6666.666667 = 0.000000
0.000000 + 0.3333333333x + x2 = 0 + 6666.666667
0.3333333333x + x2 = 0 + 6666.666667

Combine like terms: 0 + 6666.666667 = 6666.666667
0.3333333333x + x2 = 6666.666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333x + 0.25 + x2 = 6666.666667 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = 6666.666667 + 0.25

Combine like terms: 6666.666667 + 0.25 = 6666.916667
0.25 + 0.3333333333x + x2 = 6666.916667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 6666.916667

Calculate the square root of the right side: 81.651189012

Break this problem into two subproblems by setting 
(x + 0.5) equal to 81.651189012 and -81.651189012.

Subproblem 1

x + 0.5 = 81.651189012 Simplifying x + 0.5 = 81.651189012 Reorder the terms: 0.5 + x = 81.651189012 Solving 0.5 + x = 81.651189012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 81.651189012 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 81.651189012 + -0.5 x = 81.651189012 + -0.5 Combine like terms: 81.651189012 + -0.5 = 81.151189012 x = 81.151189012 Simplifying x = 81.151189012

Subproblem 2

x + 0.5 = -81.651189012 Simplifying x + 0.5 = -81.651189012 Reorder the terms: 0.5 + x = -81.651189012 Solving 0.5 + x = -81.651189012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -81.651189012 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -81.651189012 + -0.5 x = -81.651189012 + -0.5 Combine like terms: -81.651189012 + -0.5 = -82.151189012 x = -82.151189012 Simplifying x = -82.151189012

Solution

The solution to the problem is based on the solutions from the subproblems. x = {81.151189012, -82.151189012}

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