4x^2+1320x-19800=0

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Solution for 4x^2+1320x-19800=0 equation: 


Simplifying
4x2 + 1320x + -19800 = 0

Reorder the terms:
-19800 + 1320x + 4x2 = 0

Solving
-19800 + 1320x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4950 + 330x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-4950 + 330x + x2)' equal to zero and attempt to solve:

Simplifying
-4950 + 330x + x2 = 0

Solving
-4950 + 330x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4950' to each side of the equation.
-4950 + 330x + 4950 + x2 = 0 + 4950

Reorder the terms:
-4950 + 4950 + 330x + x2 = 0 + 4950

Combine like terms: -4950 + 4950 = 0
0 + 330x + x2 = 0 + 4950
330x + x2 = 0 + 4950

Combine like terms: 0 + 4950 = 4950
330x + x2 = 4950

The x term is 330x.  Take half its coefficient (165).
Square it (27225) and add it to both sides.

Add '27225' to each side of the equation.
330x + 27225 + x2 = 4950 + 27225

Reorder the terms:
27225 + 330x + x2 = 4950 + 27225

Combine like terms: 4950 + 27225 = 32175
27225 + 330x + x2 = 32175

Factor a perfect square on the left side:
(x + 165)(x + 165) = 32175

Calculate the square root of the right side: 179.373911147

Break this problem into two subproblems by setting 
(x + 165) equal to 179.373911147 and -179.373911147.


Subproblem 1
x + 165 = 179.373911147

Simplifying
x + 165 = 179.373911147

Reorder the terms:
165 + x = 179.373911147

Solving
165 + x = 179.373911147

Solving for variable 'x'.

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

Add '-165' to each side of the equation.
165 + -165 + x = 179.373911147 + -165

Combine like terms: 165 + -165 = 0
0 + x = 179.373911147 + -165
x = 179.373911147 + -165

Combine like terms: 179.373911147 + -165 = 14.373911147
x = 14.373911147

Simplifying
x = 14.373911147


Subproblem 2
x + 165 = -179.373911147

Simplifying
x + 165 = -179.373911147

Reorder the terms:
165 + x = -179.373911147

Solving
165 + x = -179.373911147

Solving for variable 'x'.

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

Add '-165' to each side of the equation.
165 + -165 + x = -179.373911147 + -165

Combine like terms: 165 + -165 = 0
0 + x = -179.373911147 + -165
x = -179.373911147 + -165

Combine like terms: -179.373911147 + -165 = -344.373911147
x = -344.373911147

Simplifying
x = -344.373911147


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.373911147, -344.373911147}
Solution
x = {14.373911147, -344.373911147}

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