4x^2=50*(1-x)*(2-x)

Solution for 4x^2=50*(1-x)*(2-x) equation:

Simplifying
4x2 = 50(1 + -1x)(2 + -1x)

Multiply (1 + -1x) * (2 + -1x)
4x2 = 50(1(2 + -1x) + -1x * (2 + -1x))
4x2 = 50((2 * 1 + -1x * 1) + -1x * (2 + -1x))
4x2 = 50((2 + -1x) + -1x * (2 + -1x))
4x2 = 50(2 + -1x + (2 * -1x + -1x * -1x))
4x2 = 50(2 + -1x + (-2x + 1x2))

Combine like terms: -1x + -2x = -3x
4x2 = 50(2 + -3x + 1x2)
4x2 = (2 * 50 + -3x * 50 + 1x2 * 50)
4x2 = (100 + -150x + 50x2)

Solving
4x2 = 100 + -150x + 50x2

Solving for variable 'x'.

Reorder the terms:
-100 + 150x + 4x2 + -50x2 = 100 + -150x + 50x2 + -100 + 150x + -50x2

Combine like terms: 4x2 + -50x2 = -46x2
-100 + 150x + -46x2 = 100 + -150x + 50x2 + -100 + 150x + -50x2

Reorder the terms:
-100 + 150x + -46x2 = 100 + -100 + -150x + 150x + 50x2 + -50x2

Combine like terms: 100 + -100 = 0
-100 + 150x + -46x2 = 0 + -150x + 150x + 50x2 + -50x2
-100 + 150x + -46x2 = -150x + 150x + 50x2 + -50x2

Combine like terms: -150x + 150x = 0
-100 + 150x + -46x2 = 0 + 50x2 + -50x2
-100 + 150x + -46x2 = 50x2 + -50x2

Combine like terms: 50x2 + -50x2 = 0
-100 + 150x + -46x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 75x + -23x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-50 + 75x + -23x2)' equal to zero and attempt to solve:

Simplifying
-50 + 75x + -23x2 = 0

Solving
-50 + 75x + -23x2 = 0

Begin completing the square.  Divide all terms by
-23 the coefficient of the squared term: 

Divide each side by '-23'.
2.173913043 + -3.260869565x + x2 = 0

Move the constant term to the right:

Add '-2.173913043' to each side of the equation.
2.173913043 + -3.260869565x + -2.173913043 + x2 = 0 + -2.173913043

Reorder the terms:
2.173913043 + -2.173913043 + -3.260869565x + x2 = 0 + -2.173913043

Combine like terms: 2.173913043 + -2.173913043 = 0.000000000
0.000000000 + -3.260869565x + x2 = 0 + -2.173913043
-3.260869565x + x2 = 0 + -2.173913043

Combine like terms: 0 + -2.173913043 = -2.173913043
-3.260869565x + x2 = -2.173913043

The x term is -3.260869565x.  Take half its coefficient (-1.630434783).
Square it (2.658317582) and add it to both sides.

Add '2.658317582' to each side of the equation.
-3.260869565x + 2.658317582 + x2 = -2.173913043 + 2.658317582

Reorder the terms:
2.658317582 + -3.260869565x + x2 = -2.173913043 + 2.658317582

Combine like terms: -2.173913043 + 2.658317582 = 0.484404539
2.658317582 + -3.260869565x + x2 = 0.484404539

Factor a perfect square on the left side:
(x + -1.630434783)(x + -1.630434783) = 0.484404539

Calculate the square root of the right side: 0.695991766

Break this problem into two subproblems by setting 
(x + -1.630434783) equal to 0.695991766 and -0.695991766.

Subproblem 1
x + -1.630434783 = 0.695991766

Simplifying
x + -1.630434783 = 0.695991766

Reorder the terms:
-1.630434783 + x = 0.695991766

Solving
-1.630434783 + x = 0.695991766

Solving for variable 'x'.

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

Add '1.630434783' to each side of the equation.
-1.630434783 + 1.630434783 + x = 0.695991766 + 1.630434783

Combine like terms: -1.630434783 + 1.630434783 = 0.000000000
0.000000000 + x = 0.695991766 + 1.630434783
x = 0.695991766 + 1.630434783

Combine like terms: 0.695991766 + 1.630434783 = 2.326426549
x = 2.326426549

Simplifying
x = 2.326426549

Subproblem 2
x + -1.630434783 = -0.695991766

Simplifying
x + -1.630434783 = -0.695991766

Reorder the terms:
-1.630434783 + x = -0.695991766

Solving
-1.630434783 + x = -0.695991766

Solving for variable 'x'.

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

Add '1.630434783' to each side of the equation.
-1.630434783 + 1.630434783 + x = -0.695991766 + 1.630434783

Combine like terms: -1.630434783 + 1.630434783 = 0.000000000
0.000000000 + x = -0.695991766 + 1.630434783
x = -0.695991766 + 1.630434783

Combine like terms: -0.695991766 + 1.630434783 = 0.934443017
x = 0.934443017

Simplifying
x = 0.934443017

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.326426549, 0.934443017}
Solution
x = {2.326426549, 0.934443017}