-8x^2+46x+30=0

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Solution for -8x^2+46x+30=0 equation:


Simplifying
-8x2 + 46x + 30 = 0

Reorder the terms:
30 + 46x + -8x2 = 0

Solving
30 + 46x + -8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 23x + -4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(15 + 23x + -4x2)' equal to zero and attempt to solve:

Simplifying
15 + 23x + -4x2 = 0

Solving
15 + 23x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-3.75 + -5.75x + x2 = 0

Move the constant term to the right:

Add '3.75' to each side of the equation.
-3.75 + -5.75x + 3.75 + x2 = 0 + 3.75

Reorder the terms:
-3.75 + 3.75 + -5.75x + x2 = 0 + 3.75

Combine like terms: -3.75 + 3.75 = 0.00
0.00 + -5.75x + x2 = 0 + 3.75
-5.75x + x2 = 0 + 3.75

Combine like terms: 0 + 3.75 = 3.75
-5.75x + x2 = 3.75

The x term is -5.75x.  Take half its coefficient (-2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
-5.75x + 8.265625 + x2 = 3.75 + 8.265625

Reorder the terms:
8.265625 + -5.75x + x2 = 3.75 + 8.265625

Combine like terms: 3.75 + 8.265625 = 12.015625
8.265625 + -5.75x + x2 = 12.015625

Factor a perfect square on the left side:
(x + -2.875)(x + -2.875) = 12.015625

Calculate the square root of the right side: 3.466356156

Break this problem into two subproblems by setting 
(x + -2.875) equal to 3.466356156 and -3.466356156.


Subproblem 1
x + -2.875 = 3.466356156

Simplifying
x + -2.875 = 3.466356156

Reorder the terms:
-2.875 + x = 3.466356156

Solving
-2.875 + x = 3.466356156

Solving for variable 'x'.

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

Add '2.875' to each side of the equation.
-2.875 + 2.875 + x = 3.466356156 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + x = 3.466356156 + 2.875
x = 3.466356156 + 2.875

Combine like terms: 3.466356156 + 2.875 = 6.341356156
x = 6.341356156

Simplifying
x = 6.341356156


Subproblem 2
x + -2.875 = -3.466356156

Simplifying
x + -2.875 = -3.466356156

Reorder the terms:
-2.875 + x = -3.466356156

Solving
-2.875 + x = -3.466356156

Solving for variable 'x'.

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

Add '2.875' to each side of the equation.
-2.875 + 2.875 + x = -3.466356156 + 2.875

Combine like terms: -2.875 + 2.875 = 0.000
0.000 + x = -3.466356156 + 2.875
x = -3.466356156 + 2.875

Combine like terms: -3.466356156 + 2.875 = -0.591356156
x = -0.591356156

Simplifying
x = -0.591356156


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.341356156, -0.591356156}
Solution
x = {6.341356156, -0.591356156}

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