-1.5x^2+8x+10.5=0

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Solution for -1.5x^2+8x+10.5=0 equation: 


Simplifying
-1.5x2 + 8x + 10.5 = 0

Reorder the terms:
10.5 + 8x + -1.5x2 = 0

Solving
10.5 + 8x + -1.5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1.5 the coefficient of the squared term: 

Divide each side by '-1.5'.
-7 + -5.333333333x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -5.333333333x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -5.333333333x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5.333333333x + x2 = 0 + 7
-5.333333333x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-5.333333333x + x2 = 7

The x term is -5.333333333x.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333x + 7.111111113 + x2 = 7 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333x + x2 = 7 + 7.111111113

Combine like terms: 7 + 7.111111113 = 14.111111113
7.111111113 + -5.333333333x + x2 = 14.111111113

Factor a perfect square on the left side:
(x + -2.666666667)(x + -2.666666667) = 14.111111113

Calculate the square root of the right side: 3.75647589

Break this problem into two subproblems by setting 
(x + -2.666666667) equal to 3.75647589 and -3.75647589.


Subproblem 1
x + -2.666666667 = 3.75647589

Simplifying
x + -2.666666667 = 3.75647589

Reorder the terms:
-2.666666667 + x = 3.75647589

Solving
-2.666666667 + x = 3.75647589

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = 3.75647589 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = 3.75647589 + 2.666666667
x = 3.75647589 + 2.666666667

Combine like terms: 3.75647589 + 2.666666667 = 6.423142557
x = 6.423142557

Simplifying
x = 6.423142557


Subproblem 2
x + -2.666666667 = -3.75647589

Simplifying
x + -2.666666667 = -3.75647589

Reorder the terms:
-2.666666667 + x = -3.75647589

Solving
-2.666666667 + x = -3.75647589

Solving for variable 'x'.

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

Add '2.666666667' to each side of the equation.
-2.666666667 + 2.666666667 + x = -3.75647589 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + x = -3.75647589 + 2.666666667
x = -3.75647589 + 2.666666667

Combine like terms: -3.75647589 + 2.666666667 = -1.089809223
x = -1.089809223

Simplifying
x = -1.089809223


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.423142557, -1.089809223}

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