800-160*x+3*x^2=0

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Solution for 800-160*x+3*x^2=0 equation: 


Simplifying
800 + -160x + 3x2 = 0

Solving
800 + -160x + 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'.
266.6666667 + -53.33333333x + x2 = 0

Move the constant term to the right:

Add '-266.6666667' to each side of the equation.
266.6666667 + -53.33333333x + -266.6666667 + x2 = 0 + -266.6666667

Reorder the terms:
266.6666667 + -266.6666667 + -53.33333333x + x2 = 0 + -266.6666667

Combine like terms: 266.6666667 + -266.6666667 = 0.0000000
0.0000000 + -53.33333333x + x2 = 0 + -266.6666667
-53.33333333x + x2 = 0 + -266.6666667

Combine like terms: 0 + -266.6666667 = -266.6666667
-53.33333333x + x2 = -266.6666667

The x term is -53.33333333x.  Take half its coefficient (-26.66666667).
Square it (711.1111113) and add it to both sides.

Add '711.1111113' to each side of the equation.
-53.33333333x + 711.1111113 + x2 = -266.6666667 + 711.1111113

Reorder the terms:
711.1111113 + -53.33333333x + x2 = -266.6666667 + 711.1111113

Combine like terms: -266.6666667 + 711.1111113 = 444.4444446
711.1111113 + -53.33333333x + x2 = 444.4444446

Factor a perfect square on the left side:
(x + -26.66666667)(x + -26.66666667) = 444.4444446

Calculate the square root of the right side: 21.081851071

Break this problem into two subproblems by setting 
(x + -26.66666667) equal to 21.081851071 and -21.081851071.


Subproblem 1
x + -26.66666667 = 21.081851071

Simplifying
x + -26.66666667 = 21.081851071

Reorder the terms:
-26.66666667 + x = 21.081851071

Solving
-26.66666667 + x = 21.081851071

Solving for variable 'x'.

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

Add '26.66666667' to each side of the equation.
-26.66666667 + 26.66666667 + x = 21.081851071 + 26.66666667

Combine like terms: -26.66666667 + 26.66666667 = 0.00000000
0.00000000 + x = 21.081851071 + 26.66666667
x = 21.081851071 + 26.66666667

Combine like terms: 21.081851071 + 26.66666667 = 47.748517741
x = 47.748517741

Simplifying
x = 47.748517741


Subproblem 2
x + -26.66666667 = -21.081851071

Simplifying
x + -26.66666667 = -21.081851071

Reorder the terms:
-26.66666667 + x = -21.081851071

Solving
-26.66666667 + x = -21.081851071

Solving for variable 'x'.

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

Add '26.66666667' to each side of the equation.
-26.66666667 + 26.66666667 + x = -21.081851071 + 26.66666667

Combine like terms: -26.66666667 + 26.66666667 = 0.00000000
0.00000000 + x = -21.081851071 + 26.66666667
x = -21.081851071 + 26.66666667

Combine like terms: -21.081851071 + 26.66666667 = 5.584815599
x = 5.584815599

Simplifying
x = 5.584815599


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {47.748517741, 5.584815599}

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