52=5x(4-3x)

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Solution for 52=5x(4-3x) equation: 


Simplifying
52 = 5x(4 + -3x)
52 = (4 * 5x + -3x * 5x)
52 = (20x + -15x2)

Solving
52 = 20x + -15x2

Solving for variable 'x'.

Reorder the terms:
52 + -20x + 15x2 = 20x + -20x + -15x2 + 15x2

Combine like terms: 20x + -20x = 0
52 + -20x + 15x2 = 0 + -15x2 + 15x2
52 + -20x + 15x2 = -15x2 + 15x2

Combine like terms: -15x2 + 15x2 = 0
52 + -20x + 15x2 = 0

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

Divide each side by '15'.
3.466666667 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '-3.466666667' to each side of the equation.
3.466666667 + -1.333333333x + -3.466666667 + x2 = 0 + -3.466666667

Reorder the terms:
3.466666667 + -3.466666667 + -1.333333333x + x2 = 0 + -3.466666667

Combine like terms: 3.466666667 + -3.466666667 = 0.000000000
0.000000000 + -1.333333333x + x2 = 0 + -3.466666667
-1.333333333x + x2 = 0 + -3.466666667

Combine like terms: 0 + -3.466666667 = -3.466666667
-1.333333333x + x2 = -3.466666667

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = -3.466666667 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = -3.466666667 + 0.4444444442

Combine like terms: -3.466666667 + 0.4444444442 = -3.0222222228
0.4444444442 + -1.333333333x + x2 = -3.0222222228

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = -3.0222222228

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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