3x^2-7x-20000=0

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Solution for 3x^2-7x-20000=0 equation: 


Simplifying
3x2 + -7x + -20000 = 0

Reorder the terms:
-20000 + -7x + 3x2 = 0

Solving
-20000 + -7x + 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 + -2.333333333x + x2 = 0

Move the constant term to the right:

Add '6666.666667' to each side of the equation.
-6666.666667 + -2.333333333x + 6666.666667 + x2 = 0 + 6666.666667

Reorder the terms:
-6666.666667 + 6666.666667 + -2.333333333x + x2 = 0 + 6666.666667

Combine like terms: -6666.666667 + 6666.666667 = 0.000000
0.000000 + -2.333333333x + x2 = 0 + 6666.666667
-2.333333333x + x2 = 0 + 6666.666667

Combine like terms: 0 + 6666.666667 = 6666.666667
-2.333333333x + x2 = 6666.666667

The x term is -2.333333333x.  Take half its coefficient (-1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
-2.333333333x + 1.361111112 + x2 = 6666.666667 + 1.361111112

Reorder the terms:
1.361111112 + -2.333333333x + x2 = 6666.666667 + 1.361111112

Combine like terms: 6666.666667 + 1.361111112 = 6668.027778112
1.361111112 + -2.333333333x + x2 = 6668.027778112

Factor a perfect square on the left side:
(x + -1.166666667)(x + -1.166666667) = 6668.027778112

Calculate the square root of the right side: 81.657992739

Break this problem into two subproblems by setting 
(x + -1.166666667) equal to 81.657992739 and -81.657992739.


Subproblem 1
x + -1.166666667 = 81.657992739

Simplifying
x + -1.166666667 = 81.657992739

Reorder the terms:
-1.166666667 + x = 81.657992739

Solving
-1.166666667 + x = 81.657992739

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = 81.657992739 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = 81.657992739 + 1.166666667
x = 81.657992739 + 1.166666667

Combine like terms: 81.657992739 + 1.166666667 = 82.824659406
x = 82.824659406

Simplifying
x = 82.824659406


Subproblem 2
x + -1.166666667 = -81.657992739

Simplifying
x + -1.166666667 = -81.657992739

Reorder the terms:
-1.166666667 + x = -81.657992739

Solving
-1.166666667 + x = -81.657992739

Solving for variable 'x'.

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

Add '1.166666667' to each side of the equation.
-1.166666667 + 1.166666667 + x = -81.657992739 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + x = -81.657992739 + 1.166666667
x = -81.657992739 + 1.166666667

Combine like terms: -81.657992739 + 1.166666667 = -80.491326072
x = -80.491326072

Simplifying
x = -80.491326072


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {82.824659406, -80.491326072}

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