2b^2=7b+49

Solution for 2b^2=7b+49 equation:

Simplifying
2b2 = 7b + 49

Reorder the terms:
2b2 = 49 + 7b

Solving
2b2 = 49 + 7b

Solving for variable 'b'.

Reorder the terms:
-49 + -7b + 2b2 = 49 + 7b + -49 + -7b

Reorder the terms:
-49 + -7b + 2b2 = 49 + -49 + 7b + -7b

Combine like terms: 49 + -49 = 0
-49 + -7b + 2b2 = 0 + 7b + -7b
-49 + -7b + 2b2 = 7b + -7b

Combine like terms: 7b + -7b = 0
-49 + -7b + 2b2 = 0

Factor a trinomial.
(-7 + -2b)(7 + -1b) = 0

Subproblem 1
Set the factor '(-7 + -2b)' equal to zero and attempt to solve:

Simplifying
-7 + -2b = 0

Solving
-7 + -2b = 0

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

Add '7' to each side of the equation.
-7 + 7 + -2b = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2b = 0 + 7
-2b = 0 + 7

Combine like terms: 0 + 7 = 7
-2b = 7

Divide each side by '-2'.
b = -3.5

Simplifying
b = -3.5
Subproblem 2
Set the factor '(7 + -1b)' equal to zero and attempt to solve:

Simplifying
7 + -1b = 0

Solving
7 + -1b = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1b = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1b = 0 + -7
-1b = 0 + -7

Combine like terms: 0 + -7 = -7
-1b = -7

Divide each side by '-1'.
b = 7

Simplifying
b = 7
Solution
b = {-3.5, 7}