(4.3x^2-2.6x-3.1)+(-7x^2-4.7x+8.4)=0

Solution for (4.3x^2-2.6x-3.1)+(-7x^2-4.7x+8.4)=0 equation:

Simplifying
(4.3x2 + -2.6x + -3.1) + (-7x2 + -4.7x + 8.4) = 0

Reorder the terms:
(-3.1 + -2.6x + 4.3x2) + (-7x2 + -4.7x + 8.4) = 0

Remove parenthesis around (-3.1 + -2.6x + 4.3x2)
-3.1 + -2.6x + 4.3x2 + (-7x2 + -4.7x + 8.4) = 0

Reorder the terms:
-3.1 + -2.6x + 4.3x2 + (8.4 + -4.7x + -7x2) = 0

Remove parenthesis around (8.4 + -4.7x + -7x2)
-3.1 + -2.6x + 4.3x2 + 8.4 + -4.7x + -7x2 = 0

Reorder the terms:
-3.1 + 8.4 + -2.6x + -4.7x + 4.3x2 + -7x2 = 0

Combine like terms: -3.1 + 8.4 = 5.3
5.3 + -2.6x + -4.7x + 4.3x2 + -7x2 = 0

Combine like terms: -2.6x + -4.7x = -7.3x
5.3 + -7.3x + 4.3x2 + -7x2 = 0

Combine like terms: 4.3x2 + -7x2 = -2.7x2
5.3 + -7.3x + -2.7x2 = 0

Solving
5.3 + -7.3x + -2.7x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2.7 the coefficient of the squared term: 

Divide each side by '-2.7'.
-1.962962963 + 2.703703704x + x2 = 0

Move the constant term to the right:

Add '1.962962963' to each side of the equation.
-1.962962963 + 2.703703704x + 1.962962963 + x2 = 0 + 1.962962963

Reorder the terms:
-1.962962963 + 1.962962963 + 2.703703704x + x2 = 0 + 1.962962963

Combine like terms: -1.962962963 + 1.962962963 = 0.000000000
0.000000000 + 2.703703704x + x2 = 0 + 1.962962963
2.703703704x + x2 = 0 + 1.962962963

Combine like terms: 0 + 1.962962963 = 1.962962963
2.703703704x + x2 = 1.962962963

The x term is 2.703703704x.  Take half its coefficient (1.351851852).
Square it (1.827503430) and add it to both sides.

Add '1.827503430' to each side of the equation.
2.703703704x + 1.827503430 + x2 = 1.962962963 + 1.827503430

Reorder the terms:
1.827503430 + 2.703703704x + x2 = 1.962962963 + 1.827503430

Combine like terms: 1.962962963 + 1.827503430 = 3.790466393
1.827503430 + 2.703703704x + x2 = 3.790466393

Factor a perfect square on the left side:
(x + 1.351851852)(x + 1.351851852) = 3.790466393

Calculate the square root of the right side: 1.946912015

Break this problem into two subproblems by setting 
(x + 1.351851852) equal to 1.946912015 and -1.946912015.

Subproblem 1
x + 1.351851852 = 1.946912015

Simplifying
x + 1.351851852 = 1.946912015

Reorder the terms:
1.351851852 + x = 1.946912015

Solving
1.351851852 + x = 1.946912015

Solving for variable 'x'.

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

Add '-1.351851852' to each side of the equation.
1.351851852 + -1.351851852 + x = 1.946912015 + -1.351851852

Combine like terms: 1.351851852 + -1.351851852 = 0.000000000
0.000000000 + x = 1.946912015 + -1.351851852
x = 1.946912015 + -1.351851852

Combine like terms: 1.946912015 + -1.351851852 = 0.595060163
x = 0.595060163

Simplifying
x = 0.595060163

Subproblem 2
x + 1.351851852 = -1.946912015

Simplifying
x + 1.351851852 = -1.946912015

Reorder the terms:
1.351851852 + x = -1.946912015

Solving
1.351851852 + x = -1.946912015

Solving for variable 'x'.

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

Add '-1.351851852' to each side of the equation.
1.351851852 + -1.351851852 + x = -1.946912015 + -1.351851852

Combine like terms: 1.351851852 + -1.351851852 = 0.000000000
0.000000000 + x = -1.946912015 + -1.351851852
x = -1.946912015 + -1.351851852

Combine like terms: -1.946912015 + -1.351851852 = -3.298763867
x = -3.298763867

Simplifying
x = -3.298763867

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.595060163, -3.298763867}