2b^2-3b-209=0

Solution for 2b^2-3b-209=0 equation:

Simplifying
2b2 + -3b + -209 = 0

Reorder the terms:
-209 + -3b + 2b2 = 0

Solving
-209 + -3b + 2b2 = 0

Solving for variable 'b'.

Factor a trinomial.
(-19 + -2b)(11 + -1b) = 0

Subproblem 1
Set the factor '(-19 + -2b)' equal to zero and attempt to solve:

Simplifying
-19 + -2b = 0

Solving
-19 + -2b = 0

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

Add '19' to each side of the equation.
-19 + 19 + -2b = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -2b = 0 + 19
-2b = 0 + 19

Combine like terms: 0 + 19 = 19
-2b = 19

Divide each side by '-2'.
b = -9.5

Simplifying
b = -9.5
Subproblem 2
Set the factor '(11 + -1b)' equal to zero and attempt to solve:

Simplifying
11 + -1b = 0

Solving
11 + -1b = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1b = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1b = 0 + -11
-1b = 0 + -11

Combine like terms: 0 + -11 = -11
-1b = -11

Divide each side by '-1'.
b = 11

Simplifying
b = 11
Solution
b = {-9.5, 11}