8x^2+10x=105

Solution for 8x^2+10x=105 equation:

Simplifying
8x2 + 10x = 105

Reorder the terms:
10x + 8x2 = 105

Solving
10x + 8x2 = 105

Solving for variable 'x'.

Reorder the terms:
-105 + 10x + 8x2 = 105 + -105

Combine like terms: 105 + -105 = 0
-105 + 10x + 8x2 = 0

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

Divide each side by '8'.
-13.125 + 1.25x + x2 = 0

Move the constant term to the right:

Add '13.125' to each side of the equation.
-13.125 + 1.25x + 13.125 + x2 = 0 + 13.125

Reorder the terms:
-13.125 + 13.125 + 1.25x + x2 = 0 + 13.125

Combine like terms: -13.125 + 13.125 = 0.000
0.000 + 1.25x + x2 = 0 + 13.125
1.25x + x2 = 0 + 13.125

Combine like terms: 0 + 13.125 = 13.125
1.25x + x2 = 13.125

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 13.125 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 13.125 + 0.390625

Combine like terms: 13.125 + 0.390625 = 13.515625
0.390625 + 1.25x + x2 = 13.515625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 13.515625

Calculate the square root of the right side: 3.676360292

Break this problem into two subproblems by setting 
(x + 0.625) equal to 3.676360292 and -3.676360292.

Subproblem 1
x + 0.625 = 3.676360292

Simplifying
x + 0.625 = 3.676360292

Reorder the terms:
0.625 + x = 3.676360292

Solving
0.625 + x = 3.676360292

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 3.676360292 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 3.676360292 + -0.625
x = 3.676360292 + -0.625

Combine like terms: 3.676360292 + -0.625 = 3.051360292
x = 3.051360292

Simplifying
x = 3.051360292

Subproblem 2
x + 0.625 = -3.676360292

Simplifying
x + 0.625 = -3.676360292

Reorder the terms:
0.625 + x = -3.676360292

Solving
0.625 + x = -3.676360292

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -3.676360292 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -3.676360292 + -0.625
x = -3.676360292 + -0.625

Combine like terms: -3.676360292 + -0.625 = -4.301360292
x = -4.301360292

Simplifying
x = -4.301360292

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.051360292, -4.301360292}