3x^2-195x-46590=0

Solution for 3x^2-195x-46590=0 equation:

Simplifying
3x2 + -195x + -46590 = 0

Reorder the terms:
-46590 + -195x + 3x2 = 0

Solving
-46590 + -195x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15530 + -65x + x2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-15530 + -65x + x2)' equal to zero and attempt to solve:

Simplifying
-15530 + -65x + x2 = 0

Solving
-15530 + -65x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15530' to each side of the equation.
-15530 + -65x + 15530 + x2 = 0 + 15530

Reorder the terms:
-15530 + 15530 + -65x + x2 = 0 + 15530

Combine like terms: -15530 + 15530 = 0
0 + -65x + x2 = 0 + 15530
-65x + x2 = 0 + 15530

Combine like terms: 0 + 15530 = 15530
-65x + x2 = 15530

The x term is -65x.  Take half its coefficient (-32.5).
Square it (1056.25) and add it to both sides.

Add '1056.25' to each side of the equation.
-65x + 1056.25 + x2 = 15530 + 1056.25

Reorder the terms:
1056.25 + -65x + x2 = 15530 + 1056.25

Combine like terms: 15530 + 1056.25 = 16586.25
1056.25 + -65x + x2 = 16586.25

Factor a perfect square on the left side:
(x + -32.5)(x + -32.5) = 16586.25

Calculate the square root of the right side: 128.787615864

Break this problem into two subproblems by setting 
(x + -32.5) equal to 128.787615864 and -128.787615864.

Subproblem 1
x + -32.5 = 128.787615864

Simplifying
x + -32.5 = 128.787615864

Reorder the terms:
-32.5 + x = 128.787615864

Solving
-32.5 + x = 128.787615864

Solving for variable 'x'.

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

Add '32.5' to each side of the equation.
-32.5 + 32.5 + x = 128.787615864 + 32.5

Combine like terms: -32.5 + 32.5 = 0.0
0.0 + x = 128.787615864 + 32.5
x = 128.787615864 + 32.5

Combine like terms: 128.787615864 + 32.5 = 161.287615864
x = 161.287615864

Simplifying
x = 161.287615864

Subproblem 2
x + -32.5 = -128.787615864

Simplifying
x + -32.5 = -128.787615864

Reorder the terms:
-32.5 + x = -128.787615864

Solving
-32.5 + x = -128.787615864

Solving for variable 'x'.

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

Add '32.5' to each side of the equation.
-32.5 + 32.5 + x = -128.787615864 + 32.5

Combine like terms: -32.5 + 32.5 = 0.0
0.0 + x = -128.787615864 + 32.5
x = -128.787615864 + 32.5

Combine like terms: -128.787615864 + 32.5 = -96.287615864
x = -96.287615864

Simplifying
x = -96.287615864

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {161.287615864, -96.287615864}
Solution
x = {161.287615864, -96.287615864}