4x^2+34x-138=0

Solution for 4x^2+34x-138=0 equation:

Simplifying
4x2 + 34x + -138 = 0

Reorder the terms:
-138 + 34x + 4x2 = 0

Solving
-138 + 34x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-69 + 17x + 2x2) = 0

Factor a trinomial.
2((-23 + -2x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-23 + -2x)' equal to zero and attempt to solve:

Simplifying
-23 + -2x = 0

Solving
-23 + -2x = 0

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

Add '23' to each side of the equation.
-23 + 23 + -2x = 0 + 23

Combine like terms: -23 + 23 = 0
0 + -2x = 0 + 23
-2x = 0 + 23

Combine like terms: 0 + 23 = 23
-2x = 23

Divide each side by '-2'.
x = -11.5

Simplifying
x = -11.5
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-11.5, 3}