2x^2-3x-28=0

Solution for 2x^2-3x-28=0 equation:

Simplifying
2x2 + -3x + -28 = 0

Reorder the terms:
-28 + -3x + 2x2 = 0

Solving
-28 + -3x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-14 + -1.5x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -1.5x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -1.5x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1.5x + x2 = 0 + 14
-1.5x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-1.5x + x2 = 14

The x term is -1.5x.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5x + 0.5625 + x2 = 14 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 14 + 0.5625

Combine like terms: 14 + 0.5625 = 14.5625
0.5625 + -1.5x + x2 = 14.5625

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 14.5625

Calculate the square root of the right side: 3.816084381

Break this problem into two subproblems by setting 
(x + -0.75) equal to 3.816084381 and -3.816084381.

Subproblem 1
x + -0.75 = 3.816084381

Simplifying
x + -0.75 = 3.816084381

Reorder the terms:
-0.75 + x = 3.816084381

Solving
-0.75 + x = 3.816084381

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = 3.816084381 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 3.816084381 + 0.75
x = 3.816084381 + 0.75

Combine like terms: 3.816084381 + 0.75 = 4.566084381
x = 4.566084381

Simplifying
x = 4.566084381

Subproblem 2
x + -0.75 = -3.816084381

Simplifying
x + -0.75 = -3.816084381

Reorder the terms:
-0.75 + x = -3.816084381

Solving
-0.75 + x = -3.816084381

Solving for variable 'x'.

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

Add '0.75' to each side of the equation.
-0.75 + 0.75 + x = -3.816084381 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -3.816084381 + 0.75
x = -3.816084381 + 0.75

Combine like terms: -3.816084381 + 0.75 = -3.066084381
x = -3.066084381

Simplifying
x = -3.066084381

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.566084381, -3.066084381}