4x^2+3x+18=27

Solution for 4x^2+3x+18=27 equation:

Simplifying
4x2 + 3x + 18 = 27

Reorder the terms:
18 + 3x + 4x2 = 27

Solving
18 + 3x + 4x2 = 27

Solving for variable 'x'.

Reorder the terms:
18 + -27 + 3x + 4x2 = 27 + -27

Combine like terms: 18 + -27 = -9
-9 + 3x + 4x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-9 + 3x + 4x2 = 0

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

Divide each side by '4'.
-2.25 + 0.75x + x2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 0.75x + 2.25 + x2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 0.75x + x2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 0.75x + x2 = 0 + 2.25
0.75x + x2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
0.75x + x2 = 2.25

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 2.25 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 2.25 + 0.140625

Combine like terms: 2.25 + 0.140625 = 2.390625
0.140625 + 0.75x + x2 = 2.390625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 2.390625

Calculate the square root of the right side: 1.54616461

Break this problem into two subproblems by setting 
(x + 0.375) equal to 1.54616461 and -1.54616461.

Subproblem 1
x + 0.375 = 1.54616461

Simplifying
x + 0.375 = 1.54616461

Reorder the terms:
0.375 + x = 1.54616461

Solving
0.375 + x = 1.54616461

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 1.54616461 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 1.54616461 + -0.375
x = 1.54616461 + -0.375

Combine like terms: 1.54616461 + -0.375 = 1.17116461
x = 1.17116461

Simplifying
x = 1.17116461

Subproblem 2
x + 0.375 = -1.54616461

Simplifying
x + 0.375 = -1.54616461

Reorder the terms:
0.375 + x = -1.54616461

Solving
0.375 + x = -1.54616461

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -1.54616461 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -1.54616461 + -0.375
x = -1.54616461 + -0.375

Combine like terms: -1.54616461 + -0.375 = -1.92116461
x = -1.92116461

Simplifying
x = -1.92116461

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.17116461, -1.92116461}