(7.5*x^2+2.4x-4.6)-(x^2-3.2x-1.5)=0

Solution for (7.5*x^2+2.4x-4.6)-(x^2-3.2x-1.5)=0 equation:

Simplifying
(7.5x2 + 2.4x + -4.6) + -1(x2 + -3.2x + -1.5) = 0

Reorder the terms:
(-4.6 + 2.4x + 7.5x2) + -1(x2 + -3.2x + -1.5) = 0

Remove parenthesis around (-4.6 + 2.4x + 7.5x2)
-4.6 + 2.4x + 7.5x2 + -1(x2 + -3.2x + -1.5) = 0

Reorder the terms:
-4.6 + 2.4x + 7.5x2 + -1(-1.5 + -3.2x + x2) = 0
-4.6 + 2.4x + 7.5x2 + (-1.5 * -1 + -3.2x * -1 + x2 * -1) = 0
-4.6 + 2.4x + 7.5x2 + (1.5 + 3.2x + -1x2) = 0

Reorder the terms:
-4.6 + 1.5 + 2.4x + 3.2x + 7.5x2 + -1x2 = 0

Combine like terms: -4.6 + 1.5 = -3.1
-3.1 + 2.4x + 3.2x + 7.5x2 + -1x2 = 0

Combine like terms: 2.4x + 3.2x = 5.6x
-3.1 + 5.6x + 7.5x2 + -1x2 = 0

Combine like terms: 7.5x2 + -1x2 = 6.5x2
-3.1 + 5.6x + 6.5x2 = 0

Solving
-3.1 + 5.6x + 6.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '6.5'.
-0.4769230769 + 0.8615384615x + x2 = 0

Move the constant term to the right:

Add '0.4769230769' to each side of the equation.
-0.4769230769 + 0.8615384615x + 0.4769230769 + x2 = 0 + 0.4769230769

Reorder the terms:
-0.4769230769 + 0.4769230769 + 0.8615384615x + x2 = 0 + 0.4769230769

Combine like terms: -0.4769230769 + 0.4769230769 = 0.0000000000
0.0000000000 + 0.8615384615x + x2 = 0 + 0.4769230769
0.8615384615x + x2 = 0 + 0.4769230769

Combine like terms: 0 + 0.4769230769 = 0.4769230769
0.8615384615x + x2 = 0.4769230769

The x term is 0.8615384615x.  Take half its coefficient (0.4307692308).
Square it (0.1855621302) and add it to both sides.

Add '0.1855621302' to each side of the equation.
0.8615384615x + 0.1855621302 + x2 = 0.4769230769 + 0.1855621302

Reorder the terms:
0.1855621302 + 0.8615384615x + x2 = 0.4769230769 + 0.1855621302

Combine like terms: 0.4769230769 + 0.1855621302 = 0.6624852071
0.1855621302 + 0.8615384615x + x2 = 0.6624852071

Factor a perfect square on the left side:
(x + 0.4307692308)(x + 0.4307692308) = 0.6624852071

Calculate the square root of the right side: 0.813931943

Break this problem into two subproblems by setting 
(x + 0.4307692308) equal to 0.813931943 and -0.813931943.

Subproblem 1
x + 0.4307692308 = 0.813931943

Simplifying
x + 0.4307692308 = 0.813931943

Reorder the terms:
0.4307692308 + x = 0.813931943

Solving
0.4307692308 + x = 0.813931943

Solving for variable 'x'.

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

Add '-0.4307692308' to each side of the equation.
0.4307692308 + -0.4307692308 + x = 0.813931943 + -0.4307692308

Combine like terms: 0.4307692308 + -0.4307692308 = 0.0000000000
0.0000000000 + x = 0.813931943 + -0.4307692308
x = 0.813931943 + -0.4307692308

Combine like terms: 0.813931943 + -0.4307692308 = 0.3831627122
x = 0.3831627122

Simplifying
x = 0.3831627122

Subproblem 2
x + 0.4307692308 = -0.813931943

Simplifying
x + 0.4307692308 = -0.813931943

Reorder the terms:
0.4307692308 + x = -0.813931943

Solving
0.4307692308 + x = -0.813931943

Solving for variable 'x'.

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

Add '-0.4307692308' to each side of the equation.
0.4307692308 + -0.4307692308 + x = -0.813931943 + -0.4307692308

Combine like terms: 0.4307692308 + -0.4307692308 = 0.0000000000
0.0000000000 + x = -0.813931943 + -0.4307692308
x = -0.813931943 + -0.4307692308

Combine like terms: -0.813931943 + -0.4307692308 = -1.2447011738
x = -1.2447011738

Simplifying
x = -1.2447011738

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3831627122, -1.2447011738}