15x^2-61x+34=0

Solution for 15x^2-61x+34=0 equation:

Simplifying
15x2 + -61x + 34 = 0

Reorder the terms:
34 + -61x + 15x2 = 0

Solving
34 + -61x + 15x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + -3x)(17 + -5x) = 0

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Subproblem 2
Set the factor '(17 + -5x)' equal to zero and attempt to solve:

Simplifying
17 + -5x = 0

Solving
17 + -5x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -5x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -5x = 0 + -17
-5x = 0 + -17

Combine like terms: 0 + -17 = -17
-5x = -17

Divide each side by '-5'.
x = 3.4

Simplifying
x = 3.4
Solution
x = {0.6666666667, 3.4}