0=2x^2+3x-84

Solution for 0=2x^2+3x-84 equation:

Simplifying
0 = 2x2 + 3x + -84

Reorder the terms:
0 = -84 + 3x + 2x2

Solving
0 = -84 + 3x + 2x2

Solving for variable 'x'.

Combine like terms: 0 + 84 = 84
84 + -3x + -2x2 = -84 + 3x + 2x2 + 84 + -3x + -2x2

Reorder the terms:
84 + -3x + -2x2 = -84 + 84 + 3x + -3x + 2x2 + -2x2

Combine like terms: -84 + 84 = 0
84 + -3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2
84 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
84 + -3x + -2x2 = 0 + 2x2 + -2x2
84 + -3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
84 + -3x + -2x2 = 0

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

Divide each side by '-2'.
-42 + 1.5x + x2 = 0

Move the constant term to the right:

Add '42' to each side of the equation.
-42 + 1.5x + 42 + x2 = 0 + 42

Reorder the terms:
-42 + 42 + 1.5x + x2 = 0 + 42

Combine like terms: -42 + 42 = 0
0 + 1.5x + x2 = 0 + 42
1.5x + x2 = 0 + 42

Combine like terms: 0 + 42 = 42
1.5x + x2 = 42

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 = 42 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 42 + 0.5625

Combine like terms: 42 + 0.5625 = 42.5625
0.5625 + 1.5x + x2 = 42.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 42.5625

Calculate the square root of the right side: 6.523994175

Break this problem into two subproblems by setting 
(x + 0.75) equal to 6.523994175 and -6.523994175.

Subproblem 1
x + 0.75 = 6.523994175

Simplifying
x + 0.75 = 6.523994175

Reorder the terms:
0.75 + x = 6.523994175

Solving
0.75 + x = 6.523994175

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 = 6.523994175 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 6.523994175 + -0.75
x = 6.523994175 + -0.75

Combine like terms: 6.523994175 + -0.75 = 5.773994175
x = 5.773994175

Simplifying
x = 5.773994175

Subproblem 2
x + 0.75 = -6.523994175

Simplifying
x + 0.75 = -6.523994175

Reorder the terms:
0.75 + x = -6.523994175

Solving
0.75 + x = -6.523994175

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 = -6.523994175 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -6.523994175 + -0.75
x = -6.523994175 + -0.75

Combine like terms: -6.523994175 + -0.75 = -7.273994175
x = -7.273994175

Simplifying
x = -7.273994175

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.773994175, -7.273994175}