(2.4x+x^2)=6.4(1.8-x)(3.4-x)

Solution for (2.4x+x^2)=6.4(1.8-x)(3.4-x) equation:

Simplifying
(2.4x + x2) = 6.4(1.8 + -1x)(3.4 + -1x)

Remove parenthesis around (2.4x + x2)
2.4x + x2 = 6.4(1.8 + -1x)(3.4 + -1x)

Multiply (1.8 + -1x) * (3.4 + -1x)
2.4x + x2 = 6.4(1.8(3.4 + -1x) + -1x * (3.4 + -1x))
2.4x + x2 = 6.4((3.4 * 1.8 + -1x * 1.8) + -1x * (3.4 + -1x))
2.4x + x2 = 6.4((6.12 + -1.8x) + -1x * (3.4 + -1x))
2.4x + x2 = 6.4(6.12 + -1.8x + (3.4 * -1x + -1x * -1x))
2.4x + x2 = 6.4(6.12 + -1.8x + (-3.4x + 1x2))

Combine like terms: -1.8x + -3.4x = -5.2x
2.4x + x2 = 6.4(6.12 + -5.2x + 1x2)
2.4x + x2 = (6.12 * 6.4 + -5.2x * 6.4 + 1x2 * 6.4)
2.4x + x2 = (39.168 + -33.28x + 6.4x2)

Solving
2.4x + x2 = 39.168 + -33.28x + 6.4x2

Solving for variable 'x'.

Reorder the terms:
-39.168 + 2.4x + 33.28x + x2 + -6.4x2 = 39.168 + -33.28x + 6.4x2 + -39.168 + 33.28x + -6.4x2

Combine like terms: 2.4x + 33.28x = 35.68x
-39.168 + 35.68x + x2 + -6.4x2 = 39.168 + -33.28x + 6.4x2 + -39.168 + 33.28x + -6.4x2

Combine like terms: x2 + -6.4x2 = -5.4x2
-39.168 + 35.68x + -5.4x2 = 39.168 + -33.28x + 6.4x2 + -39.168 + 33.28x + -6.4x2

Reorder the terms:
-39.168 + 35.68x + -5.4x2 = 39.168 + -39.168 + -33.28x + 33.28x + 6.4x2 + -6.4x2

Combine like terms: 39.168 + -39.168 = 0.000
-39.168 + 35.68x + -5.4x2 = 0.000 + -33.28x + 33.28x + 6.4x2 + -6.4x2
-39.168 + 35.68x + -5.4x2 = -33.28x + 33.28x + 6.4x2 + -6.4x2

Combine like terms: -33.28x + 33.28x = 0.00
-39.168 + 35.68x + -5.4x2 = 0.00 + 6.4x2 + -6.4x2
-39.168 + 35.68x + -5.4x2 = 6.4x2 + -6.4x2

Combine like terms: 6.4x2 + -6.4x2 = 0.0
-39.168 + 35.68x + -5.4x2 = 0.0

Begin completing the square.  Divide all terms by
-5.4 the coefficient of the squared term: 

Divide each side by '-5.4'.
7.253333333 + -6.607407407x + x2 = 0

Move the constant term to the right:

Add '-7.253333333' to each side of the equation.
7.253333333 + -6.607407407x + -7.253333333 + x2 = 0 + -7.253333333

Reorder the terms:
7.253333333 + -7.253333333 + -6.607407407x + x2 = 0 + -7.253333333

Combine like terms: 7.253333333 + -7.253333333 = 0.000000000
0.000000000 + -6.607407407x + x2 = 0 + -7.253333333
-6.607407407x + x2 = 0 + -7.253333333

Combine like terms: 0 + -7.253333333 = -7.253333333
-6.607407407x + x2 = -7.253333333

The x term is -6.607407407x.  Take half its coefficient (-3.303703704).
Square it (10.91445816) and add it to both sides.

Add '10.91445816' to each side of the equation.
-6.607407407x + 10.91445816 + x2 = -7.253333333 + 10.91445816

Reorder the terms:
10.91445816 + -6.607407407x + x2 = -7.253333333 + 10.91445816

Combine like terms: -7.253333333 + 10.91445816 = 3.661124827
10.91445816 + -6.607407407x + x2 = 3.661124827

Factor a perfect square on the left side:
(x + -3.303703704)(x + -3.303703704) = 3.661124827

Calculate the square root of the right side: 1.913406603

Break this problem into two subproblems by setting 
(x + -3.303703704) equal to 1.913406603 and -1.913406603.

Subproblem 1
x + -3.303703704 = 1.913406603

Simplifying
x + -3.303703704 = 1.913406603

Reorder the terms:
-3.303703704 + x = 1.913406603

Solving
-3.303703704 + x = 1.913406603

Solving for variable 'x'.

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

Add '3.303703704' to each side of the equation.
-3.303703704 + 3.303703704 + x = 1.913406603 + 3.303703704

Combine like terms: -3.303703704 + 3.303703704 = 0.000000000
0.000000000 + x = 1.913406603 + 3.303703704
x = 1.913406603 + 3.303703704

Combine like terms: 1.913406603 + 3.303703704 = 5.217110307
x = 5.217110307

Simplifying
x = 5.217110307

Subproblem 2
x + -3.303703704 = -1.913406603

Simplifying
x + -3.303703704 = -1.913406603

Reorder the terms:
-3.303703704 + x = -1.913406603

Solving
-3.303703704 + x = -1.913406603

Solving for variable 'x'.

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

Add '3.303703704' to each side of the equation.
-3.303703704 + 3.303703704 + x = -1.913406603 + 3.303703704

Combine like terms: -3.303703704 + 3.303703704 = 0.000000000
0.000000000 + x = -1.913406603 + 3.303703704
x = -1.913406603 + 3.303703704

Combine like terms: -1.913406603 + 3.303703704 = 1.390297101
x = 1.390297101

Simplifying
x = 1.390297101

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.217110307, 1.390297101}