210x^2-1680x+7700=0

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Solution for 210x^2-1680x+7700=0 equation: 


Simplifying
210x2 + -1680x + 7700 = 0

Reorder the terms:
7700 + -1680x + 210x2 = 0

Solving
7700 + -1680x + 210x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '70'.
70(110 + -24x + 3x2) = 0

Ignore the factor 70.

Subproblem 1
Set the factor '(110 + -24x + 3x2)' equal to zero and attempt to solve:

Simplifying
110 + -24x + 3x2 = 0

Solving
110 + -24x + 3x2 = 0

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

Divide each side by '3'.
36.66666667 + -8x + x2 = 0

Move the constant term to the right:

Add '-36.66666667' to each side of the equation.
36.66666667 + -8x + -36.66666667 + x2 = 0 + -36.66666667

Reorder the terms:
36.66666667 + -36.66666667 + -8x + x2 = 0 + -36.66666667

Combine like terms: 36.66666667 + -36.66666667 = 0.00000000
0.00000000 + -8x + x2 = 0 + -36.66666667
-8x + x2 = 0 + -36.66666667

Combine like terms: 0 + -36.66666667 = -36.66666667
-8x + x2 = -36.66666667

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 = -36.66666667 + 16

Reorder the terms:
16 + -8x + x2 = -36.66666667 + 16

Combine like terms: -36.66666667 + 16 = -20.66666667
16 + -8x + x2 = -20.66666667

Factor a perfect square on the left side:
(x + -4)(x + -4) = -20.66666667

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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