-6x^2+3x+40=0

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Solution for -6x^2+3x+40=0 equation: 


Simplifying
-6x2 + 3x + 40 = 0

Reorder the terms:
40 + 3x + -6x2 = 0

Solving
40 + 3x + -6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-6.666666667 + -0.5x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + -0.5x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + -0.5x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + -0.5x + x2 = 0 + 6.666666667
-0.5x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
-0.5x + x2 = 6.666666667

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 6.666666667 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 6.666666667 + 0.0625

Combine like terms: 6.666666667 + 0.0625 = 6.729166667
0.0625 + -0.5x + x2 = 6.729166667

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 6.729166667

Calculate the square root of the right side: 2.594063736

Break this problem into two subproblems by setting 
(x + -0.25) equal to 2.594063736 and -2.594063736.


Subproblem 1
x + -0.25 = 2.594063736

Simplifying
x + -0.25 = 2.594063736

Reorder the terms:
-0.25 + x = 2.594063736

Solving
-0.25 + x = 2.594063736

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 2.594063736 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 2.594063736 + 0.25
x = 2.594063736 + 0.25

Combine like terms: 2.594063736 + 0.25 = 2.844063736
x = 2.844063736

Simplifying
x = 2.844063736


Subproblem 2
x + -0.25 = -2.594063736

Simplifying
x + -0.25 = -2.594063736

Reorder the terms:
-0.25 + x = -2.594063736

Solving
-0.25 + x = -2.594063736

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -2.594063736 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -2.594063736 + 0.25
x = -2.594063736 + 0.25

Combine like terms: -2.594063736 + 0.25 = -2.344063736
x = -2.344063736

Simplifying
x = -2.344063736


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.844063736, -2.344063736}

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