6x^2+17x-39=0

Solution for 6x^2+17x-39=0 equation:

Simplifying
6x2 + 17x + -39 = 0

Reorder the terms:
-39 + 17x + 6x2 = 0

Solving
-39 + 17x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-13 + -3x)(3 + -2x) = 0

Subproblem 1
Set the factor '(-13 + -3x)' equal to zero and attempt to solve:

Simplifying
-13 + -3x = 0

Solving
-13 + -3x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -3x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -3x = 0 + 13
-3x = 0 + 13

Combine like terms: 0 + 13 = 13
-3x = 13

Divide each side by '-3'.
x = -4.333333333

Simplifying
x = -4.333333333
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-4.333333333, 1.5}