2x-10=6x^2

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Solution for 2x-10=6x^2 equation: 


Simplifying
2x + -10 = 6x2

Reorder the terms:
-10 + 2x = 6x2

Solving
-10 + 2x = 6x2

Solving for variable 'x'.

Combine like terms: 6x2 + -6x2 = 0
-10 + 2x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + x + -3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + x + -3x2)' equal to zero and attempt to solve:

Simplifying
-5 + x + -3x2 = 0

Solving
-5 + x + -3x2 = 0

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

Divide each side by '-3'.
1.666666667 + -0.3333333333x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -0.3333333333x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -0.3333333333x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -0.3333333333x + x2 = 0 + -1.666666667
-0.3333333333x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-0.3333333333x + x2 = -1.666666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.3333333333x + 0.25 + x2 = -1.666666667 + 0.25

Reorder the terms:
0.25 + -0.3333333333x + x2 = -1.666666667 + 0.25

Combine like terms: -1.666666667 + 0.25 = -1.416666667
0.25 + -0.3333333333x + x2 = -1.416666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -1.416666667

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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