85=2x^2+3x-84

Solution for 85=2x^2+3x-84 equation:

Simplifying
85 = 2x2 + 3x + -84

Reorder the terms:
85 = -84 + 3x + 2x2

Solving
85 = -84 + 3x + 2x2

Solving for variable 'x'.

Combine like terms: 85 + 84 = 169
169 + -3x + -2x2 = -84 + 3x + 2x2 + 84 + -3x + -2x2

Reorder the terms:
169 + -3x + -2x2 = -84 + 84 + 3x + -3x + 2x2 + -2x2

Combine like terms: -84 + 84 = 0
169 + -3x + -2x2 = 0 + 3x + -3x + 2x2 + -2x2
169 + -3x + -2x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
169 + -3x + -2x2 = 0 + 2x2 + -2x2
169 + -3x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
169 + -3x + -2x2 = 0

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

Divide each side by '-2'.
-84.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '84.5' to each side of the equation.
-84.5 + 1.5x + 84.5 + x2 = 0 + 84.5

Reorder the terms:
-84.5 + 84.5 + 1.5x + x2 = 0 + 84.5

Combine like terms: -84.5 + 84.5 = 0.0
0.0 + 1.5x + x2 = 0 + 84.5
1.5x + x2 = 0 + 84.5

Combine like terms: 0 + 84.5 = 84.5
1.5x + x2 = 84.5

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 = 84.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 84.5 + 0.5625

Combine like terms: 84.5 + 0.5625 = 85.0625
0.5625 + 1.5x + x2 = 85.0625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 85.0625

Calculate the square root of the right side: 9.222933373

Break this problem into two subproblems by setting 
(x + 0.75) equal to 9.222933373 and -9.222933373.

Subproblem 1
x + 0.75 = 9.222933373

Simplifying
x + 0.75 = 9.222933373

Reorder the terms:
0.75 + x = 9.222933373

Solving
0.75 + x = 9.222933373

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 = 9.222933373 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 9.222933373 + -0.75
x = 9.222933373 + -0.75

Combine like terms: 9.222933373 + -0.75 = 8.472933373
x = 8.472933373

Simplifying
x = 8.472933373

Subproblem 2
x + 0.75 = -9.222933373

Simplifying
x + 0.75 = -9.222933373

Reorder the terms:
0.75 + x = -9.222933373

Solving
0.75 + x = -9.222933373

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 = -9.222933373 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -9.222933373 + -0.75
x = -9.222933373 + -0.75

Combine like terms: -9.222933373 + -0.75 = -9.972933373
x = -9.972933373

Simplifying
x = -9.972933373

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.472933373, -9.972933373}