8x^2+50x-34=0

Solution for 8x^2+50x-34=0 equation:

Simplifying
8x2 + 50x + -34 = 0

Reorder the terms:
-34 + 50x + 8x2 = 0

Solving
-34 + 50x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 25x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + 25x + 4x2)' equal to zero and attempt to solve:

Simplifying
-17 + 25x + 4x2 = 0

Solving
-17 + 25x + 4x2 = 0

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

Divide each side by '4'.
-4.25 + 6.25x + x2 = 0

Move the constant term to the right:

Add '4.25' to each side of the equation.
-4.25 + 6.25x + 4.25 + x2 = 0 + 4.25

Reorder the terms:
-4.25 + 4.25 + 6.25x + x2 = 0 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + 6.25x + x2 = 0 + 4.25
6.25x + x2 = 0 + 4.25

Combine like terms: 0 + 4.25 = 4.25
6.25x + x2 = 4.25

The x term is 6.25x.  Take half its coefficient (3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
6.25x + 9.765625 + x2 = 4.25 + 9.765625

Reorder the terms:
9.765625 + 6.25x + x2 = 4.25 + 9.765625

Combine like terms: 4.25 + 9.765625 = 14.015625
9.765625 + 6.25x + x2 = 14.015625

Factor a perfect square on the left side:
(x + 3.125)(x + 3.125) = 14.015625

Calculate the square root of the right side: 3.743744783

Break this problem into two subproblems by setting 
(x + 3.125) equal to 3.743744783 and -3.743744783.

Subproblem 1
x + 3.125 = 3.743744783

Simplifying
x + 3.125 = 3.743744783

Reorder the terms:
3.125 + x = 3.743744783

Solving
3.125 + x = 3.743744783

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = 3.743744783 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = 3.743744783 + -3.125
x = 3.743744783 + -3.125

Combine like terms: 3.743744783 + -3.125 = 0.618744783
x = 0.618744783

Simplifying
x = 0.618744783

Subproblem 2
x + 3.125 = -3.743744783

Simplifying
x + 3.125 = -3.743744783

Reorder the terms:
3.125 + x = -3.743744783

Solving
3.125 + x = -3.743744783

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = -3.743744783 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = -3.743744783 + -3.125
x = -3.743744783 + -3.125

Combine like terms: -3.743744783 + -3.125 = -6.868744783
x = -6.868744783

Simplifying
x = -6.868744783

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.618744783, -6.868744783}
Solution
x = {0.618744783, -6.868744783}