4b^2-24b+11=0

Solution for 4b^2-24b+11=0 equation:

Simplifying
4b2 + -24b + 11 = 0

Reorder the terms:
11 + -24b + 4b2 = 0

Solving
11 + -24b + 4b2 = 0

Solving for variable 'b'.

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

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

Simplifying
1 + -2b = 0

Solving
1 + -2b = 0

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

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

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

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

Divide each side by '-2'.
b = 0.5

Simplifying
b = 0.5
Subproblem 2
Set the factor '(11 + -2b)' equal to zero and attempt to solve:

Simplifying
11 + -2b = 0

Solving
11 + -2b = 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 + -2b = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -2b = 0 + -11
-2b = 0 + -11

Combine like terms: 0 + -11 = -11
-2b = -11

Divide each side by '-2'.
b = 5.5

Simplifying
b = 5.5
Solution
b = {0.5, 5.5}