5x^2+75x+8=0

Solution for 5x^2+75x+8=0 equation:

Simplifying
5x2 + 75x + 8 = 0

Reorder the terms:
8 + 75x + 5x2 = 0

Solving
8 + 75x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
1.6 + 15x + x2 = 0

Move the constant term to the right:

Add '-1.6' to each side of the equation.
1.6 + 15x + -1.6 + x2 = 0 + -1.6

Reorder the terms:
1.6 + -1.6 + 15x + x2 = 0 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + 15x + x2 = 0 + -1.6
15x + x2 = 0 + -1.6

Combine like terms: 0 + -1.6 = -1.6
15x + x2 = -1.6

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -1.6 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -1.6 + 56.25

Combine like terms: -1.6 + 56.25 = 54.65
56.25 + 15x + x2 = 54.65

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 54.65

Calculate the square root of the right side: 7.392563831

Break this problem into two subproblems by setting 
(x + 7.5) equal to 7.392563831 and -7.392563831.

Subproblem 1
x + 7.5 = 7.392563831

Simplifying
x + 7.5 = 7.392563831

Reorder the terms:
7.5 + x = 7.392563831

Solving
7.5 + x = 7.392563831

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 7.392563831 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 7.392563831 + -7.5
x = 7.392563831 + -7.5

Combine like terms: 7.392563831 + -7.5 = -0.107436169
x = -0.107436169

Simplifying
x = -0.107436169

Subproblem 2
x + 7.5 = -7.392563831

Simplifying
x + 7.5 = -7.392563831

Reorder the terms:
7.5 + x = -7.392563831

Solving
7.5 + x = -7.392563831

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -7.392563831 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -7.392563831 + -7.5
x = -7.392563831 + -7.5

Combine like terms: -7.392563831 + -7.5 = -14.892563831
x = -14.892563831

Simplifying
x = -14.892563831

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.107436169, -14.892563831}