(-4X^2+X+5)+(4-3X-X^2)=0

Solution for (-4X^2+X+5)+(4-3X-X^2)=0 equation:

Simplifying
(-4X2 + X + 5) + (4 + -3X + -1X2) = 0

Reorder the terms:
(5 + X + -4X2) + (4 + -3X + -1X2) = 0

Remove parenthesis around (5 + X + -4X2)
5 + X + -4X2 + (4 + -3X + -1X2) = 0

Remove parenthesis around (4 + -3X + -1X2)
5 + X + -4X2 + 4 + -3X + -1X2 = 0

Reorder the terms:
5 + 4 + X + -3X + -4X2 + -1X2 = 0

Combine like terms: 5 + 4 = 9
9 + X + -3X + -4X2 + -1X2 = 0

Combine like terms: X + -3X = -2X
9 + -2X + -4X2 + -1X2 = 0

Combine like terms: -4X2 + -1X2 = -5X2
9 + -2X + -5X2 = 0

Solving
9 + -2X + -5X2 = 0

Solving for variable 'X'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-1.8 + 0.4X + X2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + 0.4X + 1.8 + X2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + 0.4X + X2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + 0.4X + X2 = 0 + 1.8
0.4X + X2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
0.4X + X2 = 1.8

The X term is 0.4X.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4X + 0.04 + X2 = 1.8 + 0.04

Reorder the terms:
0.04 + 0.4X + X2 = 1.8 + 0.04

Combine like terms: 1.8 + 0.04 = 1.84
0.04 + 0.4X + X2 = 1.84

Factor a perfect square on the left side:
(X + 0.2)(X + 0.2) = 1.84

Calculate the square root of the right side: 1.356465997

Break this problem into two subproblems by setting 
(X + 0.2) equal to 1.356465997 and -1.356465997.

Subproblem 1
X + 0.2 = 1.356465997

Simplifying
X + 0.2 = 1.356465997

Reorder the terms:
0.2 + X = 1.356465997

Solving
0.2 + X = 1.356465997

Solving for variable 'X'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + X = 1.356465997 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + X = 1.356465997 + -0.2
X = 1.356465997 + -0.2

Combine like terms: 1.356465997 + -0.2 = 1.156465997
X = 1.156465997

Simplifying
X = 1.156465997

Subproblem 2
X + 0.2 = -1.356465997

Simplifying
X + 0.2 = -1.356465997

Reorder the terms:
0.2 + X = -1.356465997

Solving
0.2 + X = -1.356465997

Solving for variable 'X'.

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

Add '-0.2' to each side of the equation.
0.2 + -0.2 + X = -1.356465997 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + X = -1.356465997 + -0.2
X = -1.356465997 + -0.2

Combine like terms: -1.356465997 + -0.2 = -1.556465997
X = -1.556465997

Simplifying
X = -1.556465997

Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {1.156465997, -1.556465997}