-3x^2+5x+20=0

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Solution for -3x^2+5x+20=0 equation: 


Simplifying
-3x2 + 5x + 20 = 0

Reorder the terms:
20 + 5x + -3x2 = 0

Solving
20 + 5x + -3x2 = 0

Solving for variable 'x'.

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

Divide each side by '-3'.
-6.666666667 + -1.666666667x + x2 = 0

Move the constant term to the right:

Add '6.666666667' to each side of the equation.
-6.666666667 + -1.666666667x + 6.666666667 + x2 = 0 + 6.666666667

Reorder the terms:
-6.666666667 + 6.666666667 + -1.666666667x + x2 = 0 + 6.666666667

Combine like terms: -6.666666667 + 6.666666667 = 0.000000000
0.000000000 + -1.666666667x + x2 = 0 + 6.666666667
-1.666666667x + x2 = 0 + 6.666666667

Combine like terms: 0 + 6.666666667 = 6.666666667
-1.666666667x + x2 = 6.666666667

The x term is -1.666666667x.  Take half its coefficient (-0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
-1.666666667x + 0.6944444447 + x2 = 6.666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + -1.666666667x + x2 = 6.666666667 + 0.6944444447

Combine like terms: 6.666666667 + 0.6944444447 = 7.3611111117
0.6944444447 + -1.666666667x + x2 = 7.3611111117

Factor a perfect square on the left side:
(x + -0.8333333335)(x + -0.8333333335) = 7.3611111117

Calculate the square root of the right side: 2.713136766

Break this problem into two subproblems by setting 
(x + -0.8333333335) equal to 2.713136766 and -2.713136766.


Subproblem 1
x + -0.8333333335 = 2.713136766

Simplifying
x + -0.8333333335 = 2.713136766

Reorder the terms:
-0.8333333335 + x = 2.713136766

Solving
-0.8333333335 + x = 2.713136766

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = 2.713136766 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = 2.713136766 + 0.8333333335
x = 2.713136766 + 0.8333333335

Combine like terms: 2.713136766 + 0.8333333335 = 3.5464700995
x = 3.5464700995

Simplifying
x = 3.5464700995


Subproblem 2
x + -0.8333333335 = -2.713136766

Simplifying
x + -0.8333333335 = -2.713136766

Reorder the terms:
-0.8333333335 + x = -2.713136766

Solving
-0.8333333335 + x = -2.713136766

Solving for variable 'x'.

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

Add '0.8333333335' to each side of the equation.
-0.8333333335 + 0.8333333335 + x = -2.713136766 + 0.8333333335

Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000
0.0000000000 + x = -2.713136766 + 0.8333333335
x = -2.713136766 + 0.8333333335

Combine like terms: -2.713136766 + 0.8333333335 = -1.8798034325
x = -1.8798034325

Simplifying
x = -1.8798034325


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.5464700995, -1.8798034325}

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