45-4x-24x^2=0

Solution for 45-4x-24x^2=0 equation:

Simplifying
45 + -4x + -24x2 = 0

Solving
45 + -4x + -24x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-24 the coefficient of the squared term: 

Divide each side by '-24'.
-1.875 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + 0.1666666667x + 1.875 + x2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + 0.1666666667x + x2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + 0.1666666667x + x2 = 0 + 1.875
0.1666666667x + x2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
0.1666666667x + x2 = 1.875

The x term is 0.1666666667x.  Take half its coefficient (0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
0.1666666667x + 0.006944444447 + x2 = 1.875 + 0.006944444447

Reorder the terms:
0.006944444447 + 0.1666666667x + x2 = 1.875 + 0.006944444447

Combine like terms: 1.875 + 0.006944444447 = 1.881944444447
0.006944444447 + 0.1666666667x + x2 = 1.881944444447

Factor a perfect square on the left side:
(x + 0.08333333335)(x + 0.08333333335) = 1.881944444447

Calculate the square root of the right side: 1.371839803

Break this problem into two subproblems by setting 
(x + 0.08333333335) equal to 1.371839803 and -1.371839803.

Subproblem 1
x + 0.08333333335 = 1.371839803

Simplifying
x + 0.08333333335 = 1.371839803

Reorder the terms:
0.08333333335 + x = 1.371839803

Solving
0.08333333335 + x = 1.371839803

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = 1.371839803 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = 1.371839803 + -0.08333333335
x = 1.371839803 + -0.08333333335

Combine like terms: 1.371839803 + -0.08333333335 = 1.28850646965
x = 1.28850646965

Simplifying
x = 1.28850646965

Subproblem 2
x + 0.08333333335 = -1.371839803

Simplifying
x + 0.08333333335 = -1.371839803

Reorder the terms:
0.08333333335 + x = -1.371839803

Solving
0.08333333335 + x = -1.371839803

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = -1.371839803 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = -1.371839803 + -0.08333333335
x = -1.371839803 + -0.08333333335

Combine like terms: -1.371839803 + -0.08333333335 = -1.45517313635
x = -1.45517313635

Simplifying
x = -1.45517313635

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.28850646965, -1.45517313635}