(24x^2+9x-2)=0

Solution for (24x^2+9x-2)=0 equation:

Simplifying
(24x2 + 9x + -2) = 0

Reorder the terms:
(-2 + 9x + 24x2) = 0

Remove parenthesis around (-2 + 9x + 24x2)
-2 + 9x + 24x2 = 0

Solving
-2 + 9x + 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'.
-0.08333333333 + 0.375x + x2 = 0

Move the constant term to the right:

Add '0.08333333333' to each side of the equation.
-0.08333333333 + 0.375x + 0.08333333333 + x2 = 0 + 0.08333333333

Reorder the terms:
-0.08333333333 + 0.08333333333 + 0.375x + x2 = 0 + 0.08333333333

Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000
0.00000000000 + 0.375x + x2 = 0 + 0.08333333333
0.375x + x2 = 0 + 0.08333333333

Combine like terms: 0 + 0.08333333333 = 0.08333333333
0.375x + x2 = 0.08333333333

The x term is 0.375x.  Take half its coefficient (0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
0.375x + 0.03515625 + x2 = 0.08333333333 + 0.03515625

Reorder the terms:
0.03515625 + 0.375x + x2 = 0.08333333333 + 0.03515625

Combine like terms: 0.08333333333 + 0.03515625 = 0.11848958333
0.03515625 + 0.375x + x2 = 0.11848958333

Factor a perfect square on the left side:
(x + 0.1875)(x + 0.1875) = 0.11848958333

Calculate the square root of the right side: 0.344223159

Break this problem into two subproblems by setting 
(x + 0.1875) equal to 0.344223159 and -0.344223159.

Subproblem 1
x + 0.1875 = 0.344223159

Simplifying
x + 0.1875 = 0.344223159

Reorder the terms:
0.1875 + x = 0.344223159

Solving
0.1875 + x = 0.344223159

Solving for variable 'x'.

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

Add '-0.1875' to each side of the equation.
0.1875 + -0.1875 + x = 0.344223159 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + x = 0.344223159 + -0.1875
x = 0.344223159 + -0.1875

Combine like terms: 0.344223159 + -0.1875 = 0.156723159
x = 0.156723159

Simplifying
x = 0.156723159

Subproblem 2
x + 0.1875 = -0.344223159

Simplifying
x + 0.1875 = -0.344223159

Reorder the terms:
0.1875 + x = -0.344223159

Solving
0.1875 + x = -0.344223159

Solving for variable 'x'.

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

Add '-0.1875' to each side of the equation.
0.1875 + -0.1875 + x = -0.344223159 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + x = -0.344223159 + -0.1875
x = -0.344223159 + -0.1875

Combine like terms: -0.344223159 + -0.1875 = -0.531723159
x = -0.531723159

Simplifying
x = -0.531723159

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.156723159, -0.531723159}