-0.8*(X^2)+24X+6=0

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Solution for -0.8*(X^2)+24X+6=0 equation:


Simplifying
-0.8(X2) + 24X + 6 = 0

Reorder the terms:
6 + 24X + -0.8X2 = 0

Solving
6 + 24X + -0.8X2 = 0

Solving for variable 'X'.

Begin completing the square.  Divide all terms by
-0.8 the coefficient of the squared term: 

Divide each side by '-0.8'.
-7.5 + -30X + X2 = 0

Move the constant term to the right:

Add '7.5' to each side of the equation.
-7.5 + -30X + 7.5 + X2 = 0 + 7.5

Reorder the terms:
-7.5 + 7.5 + -30X + X2 = 0 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + -30X + X2 = 0 + 7.5
-30X + X2 = 0 + 7.5

Combine like terms: 0 + 7.5 = 7.5
-30X + X2 = 7.5

The X term is -30X.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30X + 225 + X2 = 7.5 + 225

Reorder the terms:
225 + -30X + X2 = 7.5 + 225

Combine like terms: 7.5 + 225 = 232.5
225 + -30X + X2 = 232.5

Factor a perfect square on the left side:
(X + -15)(X + -15) = 232.5

Calculate the square root of the right side: 15.247950682

Break this problem into two subproblems by setting 
(X + -15) equal to 15.247950682 and -15.247950682.

Subproblem 1

X + -15 = 15.247950682 Simplifying X + -15 = 15.247950682 Reorder the terms: -15 + X = 15.247950682 Solving -15 + X = 15.247950682 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + X = 15.247950682 + 15 Combine like terms: -15 + 15 = 0 0 + X = 15.247950682 + 15 X = 15.247950682 + 15 Combine like terms: 15.247950682 + 15 = 30.247950682 X = 30.247950682 Simplifying X = 30.247950682

Subproblem 2

X + -15 = -15.247950682 Simplifying X + -15 = -15.247950682 Reorder the terms: -15 + X = -15.247950682 Solving -15 + X = -15.247950682 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + X = -15.247950682 + 15 Combine like terms: -15 + 15 = 0 0 + X = -15.247950682 + 15 X = -15.247950682 + 15 Combine like terms: -15.247950682 + 15 = -0.247950682 X = -0.247950682 Simplifying X = -0.247950682

Solution

The solution to the problem is based on the solutions from the subproblems. X = {30.247950682, -0.247950682}

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