-3x^2+800x-20=

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Solution for -3x^2+800x-20= equation: 


Simplifying
-3x2 + 800x + -20 = 0

Reorder the terms:
-20 + 800x + -3x2 = 0

Solving
-20 + 800x + -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'.
6.666666667 + -266.6666667x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + -266.6666667x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + -266.6666667x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + -266.6666667x + x2 = 0 + -6.666666667
-266.6666667x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
-266.6666667x + x2 = -6.666666667

The x term is -266.6666667x.  Take half its coefficient (-133.3333334).
Square it (17777.77780) and add it to both sides.

Add '17777.77780' to each side of the equation.
-266.6666667x + 17777.77780 + x2 = -6.666666667 + 17777.77780

Reorder the terms:
17777.77780 + -266.6666667x + x2 = -6.666666667 + 17777.77780

Combine like terms: -6.666666667 + 17777.77780 = 17771.111133333
17777.77780 + -266.6666667x + x2 = 17771.111133333

Factor a perfect square on the left side:
(x + -133.3333334)(x + -133.3333334) = 17771.111133333

Calculate the square root of the right side: 133.308331072

Break this problem into two subproblems by setting 
(x + -133.3333334) equal to 133.308331072 and -133.308331072.


Subproblem 1
x + -133.3333334 = 133.308331072

Simplifying
x + -133.3333334 = 133.308331072

Reorder the terms:
-133.3333334 + x = 133.308331072

Solving
-133.3333334 + x = 133.308331072

Solving for variable 'x'.

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

Add '133.3333334' to each side of the equation.
-133.3333334 + 133.3333334 + x = 133.308331072 + 133.3333334

Combine like terms: -133.3333334 + 133.3333334 = 0.0000000
0.0000000 + x = 133.308331072 + 133.3333334
x = 133.308331072 + 133.3333334

Combine like terms: 133.308331072 + 133.3333334 = 266.641664472
x = 266.641664472

Simplifying
x = 266.641664472


Subproblem 2
x + -133.3333334 = -133.308331072

Simplifying
x + -133.3333334 = -133.308331072

Reorder the terms:
-133.3333334 + x = -133.308331072

Solving
-133.3333334 + x = -133.308331072

Solving for variable 'x'.

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

Add '133.3333334' to each side of the equation.
-133.3333334 + 133.3333334 + x = -133.308331072 + 133.3333334

Combine like terms: -133.3333334 + 133.3333334 = 0.0000000
0.0000000 + x = -133.308331072 + 133.3333334
x = -133.308331072 + 133.3333334

Combine like terms: -133.308331072 + 133.3333334 = 0.025002328
x = 0.025002328

Simplifying
x = 0.025002328


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {266.641664472, 0.025002328}

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