7x^2-3x-8=0

Solution for 7x^2-3x-8=0 equation:

Simplifying
7x2 + -3x + -8 = 0

Reorder the terms:
-8 + -3x + 7x2 = 0

Solving
-8 + -3x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-1.142857143 + -0.4285714286x + x2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + -0.4285714286x + 1.142857143 + x2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + -0.4285714286x + x2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + -0.4285714286x + x2 = 0 + 1.142857143
-0.4285714286x + x2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
-0.4285714286x + x2 = 1.142857143

The x term is -0.4285714286x.  Take half its coefficient (-0.2142857143).
Square it (0.04591836735) and add it to both sides.

Add '0.04591836735' to each side of the equation.
-0.4285714286x + 0.04591836735 + x2 = 1.142857143 + 0.04591836735

Reorder the terms:
0.04591836735 + -0.4285714286x + x2 = 1.142857143 + 0.04591836735

Combine like terms: 1.142857143 + 0.04591836735 = 1.18877551035
0.04591836735 + -0.4285714286x + x2 = 1.18877551035

Factor a perfect square on the left side:
(x + -0.2142857143)(x + -0.2142857143) = 1.18877551035

Calculate the square root of the right side: 1.090309823

Break this problem into two subproblems by setting 
(x + -0.2142857143) equal to 1.090309823 and -1.090309823.

Subproblem 1
x + -0.2142857143 = 1.090309823

Simplifying
x + -0.2142857143 = 1.090309823

Reorder the terms:
-0.2142857143 + x = 1.090309823

Solving
-0.2142857143 + x = 1.090309823

Solving for variable 'x'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + x = 1.090309823 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + x = 1.090309823 + 0.2142857143
x = 1.090309823 + 0.2142857143

Combine like terms: 1.090309823 + 0.2142857143 = 1.3045955373
x = 1.3045955373

Simplifying
x = 1.3045955373

Subproblem 2
x + -0.2142857143 = -1.090309823

Simplifying
x + -0.2142857143 = -1.090309823

Reorder the terms:
-0.2142857143 + x = -1.090309823

Solving
-0.2142857143 + x = -1.090309823

Solving for variable 'x'.

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

Add '0.2142857143' to each side of the equation.
-0.2142857143 + 0.2142857143 + x = -1.090309823 + 0.2142857143

Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000
0.0000000000 + x = -1.090309823 + 0.2142857143
x = -1.090309823 + 0.2142857143

Combine like terms: -1.090309823 + 0.2142857143 = -0.8760241087
x = -0.8760241087

Simplifying
x = -0.8760241087

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.3045955373, -0.8760241087}