3x^2-90x-4200=0

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Solution for 3x^2-90x-4200=0 equation: 


Simplifying
3x2 + -90x + -4200 = 0

Reorder the terms:
-4200 + -90x + 3x2 = 0

Solving
-4200 + -90x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1400 + -30x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-1400 + -30x + x2)' equal to zero and attempt to solve:

Simplifying
-1400 + -30x + x2 = 0

Solving
-1400 + -30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1400' to each side of the equation.
-1400 + -30x + 1400 + x2 = 0 + 1400

Reorder the terms:
-1400 + 1400 + -30x + x2 = 0 + 1400

Combine like terms: -1400 + 1400 = 0
0 + -30x + x2 = 0 + 1400
-30x + x2 = 0 + 1400

Combine like terms: 0 + 1400 = 1400
-30x + x2 = 1400

The x term is -30x.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30x + 225 + x2 = 1400 + 225

Reorder the terms:
225 + -30x + x2 = 1400 + 225

Combine like terms: 1400 + 225 = 1625
225 + -30x + x2 = 1625

Factor a perfect square on the left side:
(x + -15)(x + -15) = 1625

Calculate the square root of the right side: 40.311288741

Break this problem into two subproblems by setting 
(x + -15) equal to 40.311288741 and -40.311288741.


Subproblem 1
x + -15 = 40.311288741

Simplifying
x + -15 = 40.311288741

Reorder the terms:
-15 + x = 40.311288741

Solving
-15 + x = 40.311288741

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = 40.311288741 + 15

Combine like terms: -15 + 15 = 0
0 + x = 40.311288741 + 15
x = 40.311288741 + 15

Combine like terms: 40.311288741 + 15 = 55.311288741
x = 55.311288741

Simplifying
x = 55.311288741


Subproblem 2
x + -15 = -40.311288741

Simplifying
x + -15 = -40.311288741

Reorder the terms:
-15 + x = -40.311288741

Solving
-15 + x = -40.311288741

Solving for variable 'x'.

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

Add '15' to each side of the equation.
-15 + 15 + x = -40.311288741 + 15

Combine like terms: -15 + 15 = 0
0 + x = -40.311288741 + 15
x = -40.311288741 + 15

Combine like terms: -40.311288741 + 15 = -25.311288741
x = -25.311288741

Simplifying
x = -25.311288741


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {55.311288741, -25.311288741}
Solution
x = {55.311288741, -25.311288741}

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