20=10x-3x^2

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Solution for 20=10x-3x^2 equation: 


Simplifying
20 = 10x + -3x2

Solving
20 = 10x + -3x2

Solving for variable 'x'.

Reorder the terms:
20 + -10x + 3x2 = 10x + -10x + -3x2 + 3x2

Combine like terms: 10x + -10x = 0
20 + -10x + 3x2 = 0 + -3x2 + 3x2
20 + -10x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
20 + -10x + 3x2 = 0

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

Divide each side by '3'.
6.666666667 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + -3.333333333x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + -3.333333333x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + -3.333333333x + x2 = 0 + -6.666666667
-3.333333333x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
-3.333333333x + x2 = -6.666666667

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = -6.666666667 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = -6.666666667 + 2.777777779

Combine like terms: -6.666666667 + 2.777777779 = -3.888888888
2.777777779 + -3.333333333x + x2 = -3.888888888

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = -3.888888888

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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