4x^2+15x+9=5

Solution for 4x^2+15x+9=5 equation:

Simplifying
4x2 + 15x + 9 = 5

Reorder the terms:
9 + 15x + 4x2 = 5

Solving
9 + 15x + 4x2 = 5

Solving for variable 'x'.

Reorder the terms:
9 + -5 + 15x + 4x2 = 5 + -5

Combine like terms: 9 + -5 = 4
4 + 15x + 4x2 = 5 + -5

Combine like terms: 5 + -5 = 0
4 + 15x + 4x2 = 0

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

Divide each side by '4'.
1 + 3.75x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 3.75x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 3.75x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3.75x + x2 = 0 + -1
3.75x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
3.75x + x2 = -1

The x term is 3.75x.  Take half its coefficient (1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
3.75x + 3.515625 + x2 = -1 + 3.515625

Reorder the terms:
3.515625 + 3.75x + x2 = -1 + 3.515625

Combine like terms: -1 + 3.515625 = 2.515625
3.515625 + 3.75x + x2 = 2.515625

Factor a perfect square on the left side:
(x + 1.875)(x + 1.875) = 2.515625

Calculate the square root of the right side: 1.586072193

Break this problem into two subproblems by setting 
(x + 1.875) equal to 1.586072193 and -1.586072193.

Subproblem 1
x + 1.875 = 1.586072193

Simplifying
x + 1.875 = 1.586072193

Reorder the terms:
1.875 + x = 1.586072193

Solving
1.875 + x = 1.586072193

Solving for variable 'x'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + x = 1.586072193 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + x = 1.586072193 + -1.875
x = 1.586072193 + -1.875

Combine like terms: 1.586072193 + -1.875 = -0.288927807
x = -0.288927807

Simplifying
x = -0.288927807

Subproblem 2
x + 1.875 = -1.586072193

Simplifying
x + 1.875 = -1.586072193

Reorder the terms:
1.875 + x = -1.586072193

Solving
1.875 + x = -1.586072193

Solving for variable 'x'.

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

Add '-1.875' to each side of the equation.
1.875 + -1.875 + x = -1.586072193 + -1.875

Combine like terms: 1.875 + -1.875 = 0.000
0.000 + x = -1.586072193 + -1.875
x = -1.586072193 + -1.875

Combine like terms: -1.586072193 + -1.875 = -3.461072193
x = -3.461072193

Simplifying
x = -3.461072193

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.288927807, -3.461072193}