100=5+20*x+0.5*(-3)*x^2

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Solution for 100=5+20*x+0.5*(-3)*x^2 equation: 


Simplifying
100 = 5 + 20x + 0.5(-3) * x2

Multiply 0.5 * -3
100 = 5 + 20x + -1.5x2

Solving
100 = 5 + 20x + -1.5x2

Solving for variable 'x'.

Combine like terms: 100 + -5 = 95
95 + -20x + 1.5x2 = 5 + 20x + -1.5x2 + -5 + -20x + 1.5x2

Reorder the terms:
95 + -20x + 1.5x2 = 5 + -5 + 20x + -20x + -1.5x2 + 1.5x2

Combine like terms: 5 + -5 = 0
95 + -20x + 1.5x2 = 0 + 20x + -20x + -1.5x2 + 1.5x2
95 + -20x + 1.5x2 = 20x + -20x + -1.5x2 + 1.5x2

Combine like terms: 20x + -20x = 0
95 + -20x + 1.5x2 = 0 + -1.5x2 + 1.5x2
95 + -20x + 1.5x2 = -1.5x2 + 1.5x2

Combine like terms: -1.5x2 + 1.5x2 = 0.0
95 + -20x + 1.5x2 = 0.0

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

Divide each side by '1.5'.
63.33333333 + -13.33333333x + x2 = 0

Move the constant term to the right:

Add '-63.33333333' to each side of the equation.
63.33333333 + -13.33333333x + -63.33333333 + x2 = 0 + -63.33333333

Reorder the terms:
63.33333333 + -63.33333333 + -13.33333333x + x2 = 0 + -63.33333333

Combine like terms: 63.33333333 + -63.33333333 = 0.00000000
0.00000000 + -13.33333333x + x2 = 0 + -63.33333333
-13.33333333x + x2 = 0 + -63.33333333

Combine like terms: 0 + -63.33333333 = -63.33333333
-13.33333333x + x2 = -63.33333333

The x term is -13.33333333x.  Take half its coefficient (-6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
-13.33333333x + 44.44444442 + x2 = -63.33333333 + 44.44444442

Reorder the terms:
44.44444442 + -13.33333333x + x2 = -63.33333333 + 44.44444442

Combine like terms: -63.33333333 + 44.44444442 = -18.88888891
44.44444442 + -13.33333333x + x2 = -18.88888891

Factor a perfect square on the left side:
(x + -6.666666665)(x + -6.666666665) = -18.88888891

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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