4b^2-9b-34=0

Solution for 4b^2-9b-34=0 equation:

Simplifying
4b2 + -9b + -34 = 0

Reorder the terms:
-34 + -9b + 4b2 = 0

Solving
-34 + -9b + 4b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-2 + -1b)(17 + -4b) = 0

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

Simplifying
-2 + -1b = 0

Solving
-2 + -1b = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1b = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1b = 0 + 2
-1b = 0 + 2

Combine like terms: 0 + 2 = 2
-1b = 2

Divide each side by '-1'.
b = -2

Simplifying
b = -2
Subproblem 2
Set the factor '(17 + -4b)' equal to zero and attempt to solve:

Simplifying
17 + -4b = 0

Solving
17 + -4b = 0

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

Add '-17' to each side of the equation.
17 + -17 + -4b = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -4b = 0 + -17
-4b = 0 + -17

Combine like terms: 0 + -17 = -17
-4b = -17

Divide each side by '-4'.
b = 4.25

Simplifying
b = 4.25
Solution
b = {-2, 4.25}