120x-15x^2-250=0

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Solution for 120x-15x^2-250=0 equation: 


Simplifying
120x + -15x2 + -250 = 0

Reorder the terms:
-250 + 120x + -15x2 = 0

Solving
-250 + 120x + -15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-50 + 24x + -3x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-50 + 24x + -3x2)' equal to zero and attempt to solve:

Simplifying
-50 + 24x + -3x2 = 0

Solving
-50 + 24x + -3x2 = 0

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

Divide each side by '-3'.
16.66666667 + -8x + x2 = 0

Move the constant term to the right:

Add '-16.66666667' to each side of the equation.
16.66666667 + -8x + -16.66666667 + x2 = 0 + -16.66666667

Reorder the terms:
16.66666667 + -16.66666667 + -8x + x2 = 0 + -16.66666667

Combine like terms: 16.66666667 + -16.66666667 = 0.00000000
0.00000000 + -8x + x2 = 0 + -16.66666667
-8x + x2 = 0 + -16.66666667

Combine like terms: 0 + -16.66666667 = -16.66666667
-8x + x2 = -16.66666667

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -16.66666667 + 16

Reorder the terms:
16 + -8x + x2 = -16.66666667 + 16

Combine like terms: -16.66666667 + 16 = -0.66666667
16 + -8x + x2 = -0.66666667

Factor a perfect square on the left side:
(x + -4)(x + -4) = -0.66666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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