42x^2-482x-2460=0

Solution for 42x^2-482x-2460=0 equation:

Simplifying
42x2 + -482x + -2460 = 0

Reorder the terms:
-2460 + -482x + 42x2 = 0

Solving
-2460 + -482x + 42x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1230 + -241x + 21x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1230 + -241x + 21x2)' equal to zero and attempt to solve:

Simplifying
-1230 + -241x + 21x2 = 0

Solving
-1230 + -241x + 21x2 = 0

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

Divide each side by '21'.
-58.57142857 + -11.47619048x + x2 = 0

Move the constant term to the right:

Add '58.57142857' to each side of the equation.
-58.57142857 + -11.47619048x + 58.57142857 + x2 = 0 + 58.57142857

Reorder the terms:
-58.57142857 + 58.57142857 + -11.47619048x + x2 = 0 + 58.57142857

Combine like terms: -58.57142857 + 58.57142857 = 0.00000000
0.00000000 + -11.47619048x + x2 = 0 + 58.57142857
-11.47619048x + x2 = 0 + 58.57142857

Combine like terms: 0 + 58.57142857 = 58.57142857
-11.47619048x + x2 = 58.57142857

The x term is -11.47619048x.  Take half its coefficient (-5.73809524).
Square it (32.92573698) and add it to both sides.

Add '32.92573698' to each side of the equation.
-11.47619048x + 32.92573698 + x2 = 58.57142857 + 32.92573698

Reorder the terms:
32.92573698 + -11.47619048x + x2 = 58.57142857 + 32.92573698

Combine like terms: 58.57142857 + 32.92573698 = 91.49716555
32.92573698 + -11.47619048x + x2 = 91.49716555

Factor a perfect square on the left side:
(x + -5.73809524)(x + -5.73809524) = 91.49716555

Calculate the square root of the right side: 9.565415075

Break this problem into two subproblems by setting 
(x + -5.73809524) equal to 9.565415075 and -9.565415075.

Subproblem 1
x + -5.73809524 = 9.565415075

Simplifying
x + -5.73809524 = 9.565415075

Reorder the terms:
-5.73809524 + x = 9.565415075

Solving
-5.73809524 + x = 9.565415075

Solving for variable 'x'.

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

Add '5.73809524' to each side of the equation.
-5.73809524 + 5.73809524 + x = 9.565415075 + 5.73809524

Combine like terms: -5.73809524 + 5.73809524 = 0.00000000
0.00000000 + x = 9.565415075 + 5.73809524
x = 9.565415075 + 5.73809524

Combine like terms: 9.565415075 + 5.73809524 = 15.303510315
x = 15.303510315

Simplifying
x = 15.303510315

Subproblem 2
x + -5.73809524 = -9.565415075

Simplifying
x + -5.73809524 = -9.565415075

Reorder the terms:
-5.73809524 + x = -9.565415075

Solving
-5.73809524 + x = -9.565415075

Solving for variable 'x'.

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

Add '5.73809524' to each side of the equation.
-5.73809524 + 5.73809524 + x = -9.565415075 + 5.73809524

Combine like terms: -5.73809524 + 5.73809524 = 0.00000000
0.00000000 + x = -9.565415075 + 5.73809524
x = -9.565415075 + 5.73809524

Combine like terms: -9.565415075 + 5.73809524 = -3.827319835
x = -3.827319835

Simplifying
x = -3.827319835

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.303510315, -3.827319835}
Solution
x = {15.303510315, -3.827319835}