6x^2+10x-105=0

Solution for 6x^2+10x-105=0 equation:

Simplifying
6x2 + 10x + -105 = 0

Reorder the terms:
-105 + 10x + 6x2 = 0

Solving
-105 + 10x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-17.5 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + 1.666666667x + 17.5 + x2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + 1.666666667x + x2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + 1.666666667x + x2 = 0 + 17.5
1.666666667x + x2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
1.666666667x + x2 = 17.5

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 17.5 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 17.5 + 0.6944444447

Combine like terms: 17.5 + 0.6944444447 = 18.1944444447
0.6944444447 + 1.666666667x + x2 = 18.1944444447

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 18.1944444447

Calculate the square root of the right side: 4.265494631

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 4.265494631 and -4.265494631.

Subproblem 1
x + 0.8333333335 = 4.265494631

Simplifying
x + 0.8333333335 = 4.265494631

Reorder the terms:
0.8333333335 + x = 4.265494631

Solving
0.8333333335 + x = 4.265494631

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 4.265494631 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 4.265494631 + -0.8333333335
x = 4.265494631 + -0.8333333335

Combine like terms: 4.265494631 + -0.8333333335 = 3.4321612975
x = 3.4321612975

Simplifying
x = 3.4321612975

Subproblem 2
x + 0.8333333335 = -4.265494631

Simplifying
x + 0.8333333335 = -4.265494631

Reorder the terms:
0.8333333335 + x = -4.265494631

Solving
0.8333333335 + x = -4.265494631

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -4.265494631 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -4.265494631 + -0.8333333335
x = -4.265494631 + -0.8333333335

Combine like terms: -4.265494631 + -0.8333333335 = -5.0988279645
x = -5.0988279645

Simplifying
x = -5.0988279645

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.4321612975, -5.0988279645}