-30x^2+680x+2400=0

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Solution for -30x^2+680x+2400=0 equation: 


Simplifying
-30x2 + 680x + 2400 = 0

Reorder the terms:
2400 + 680x + -30x2 = 0

Solving
2400 + 680x + -30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(240 + 68x + -3x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(240 + 68x + -3x2)' equal to zero and attempt to solve:

Simplifying
240 + 68x + -3x2 = 0

Solving
240 + 68x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-80 + -22.66666667x + x2 = 0

Move the constant term to the right:

Add '80' to each side of the equation.
-80 + -22.66666667x + 80 + x2 = 0 + 80

Reorder the terms:
-80 + 80 + -22.66666667x + x2 = 0 + 80

Combine like terms: -80 + 80 = 0
0 + -22.66666667x + x2 = 0 + 80
-22.66666667x + x2 = 0 + 80

Combine like terms: 0 + 80 = 80
-22.66666667x + x2 = 80

The x term is -22.66666667x.  Take half its coefficient (-11.33333334).
Square it (128.4444446) and add it to both sides.

Add '128.4444446' to each side of the equation.
-22.66666667x + 128.4444446 + x2 = 80 + 128.4444446

Reorder the terms:
128.4444446 + -22.66666667x + x2 = 80 + 128.4444446

Combine like terms: 80 + 128.4444446 = 208.4444446
128.4444446 + -22.66666667x + x2 = 208.4444446

Factor a perfect square on the left side:
(x + -11.33333334)(x + -11.33333334) = 208.4444446

Calculate the square root of the right side: 14.437605224

Break this problem into two subproblems by setting 
(x + -11.33333334) equal to 14.437605224 and -14.437605224.


Subproblem 1
x + -11.33333334 = 14.437605224

Simplifying
x + -11.33333334 = 14.437605224

Reorder the terms:
-11.33333334 + x = 14.437605224

Solving
-11.33333334 + x = 14.437605224

Solving for variable 'x'.

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

Add '11.33333334' to each side of the equation.
-11.33333334 + 11.33333334 + x = 14.437605224 + 11.33333334

Combine like terms: -11.33333334 + 11.33333334 = 0.00000000
0.00000000 + x = 14.437605224 + 11.33333334
x = 14.437605224 + 11.33333334

Combine like terms: 14.437605224 + 11.33333334 = 25.770938564
x = 25.770938564

Simplifying
x = 25.770938564


Subproblem 2
x + -11.33333334 = -14.437605224

Simplifying
x + -11.33333334 = -14.437605224

Reorder the terms:
-11.33333334 + x = -14.437605224

Solving
-11.33333334 + x = -14.437605224

Solving for variable 'x'.

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

Add '11.33333334' to each side of the equation.
-11.33333334 + 11.33333334 + x = -14.437605224 + 11.33333334

Combine like terms: -11.33333334 + 11.33333334 = 0.00000000
0.00000000 + x = -14.437605224 + 11.33333334
x = -14.437605224 + 11.33333334

Combine like terms: -14.437605224 + 11.33333334 = -3.104271884
x = -3.104271884

Simplifying
x = -3.104271884


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {25.770938564, -3.104271884}
Solution
x = {25.770938564, -3.104271884}

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