7b^2=-14+51b

Solution for 7b^2=-14+51b equation:

Simplifying
7b2 = -14 + 51b

Solving
7b2 = -14 + 51b

Solving for variable 'b'.

Reorder the terms:
14 + -51b + 7b2 = -14 + 51b + 14 + -51b

Reorder the terms:
14 + -51b + 7b2 = -14 + 14 + 51b + -51b

Combine like terms: -14 + 14 = 0
14 + -51b + 7b2 = 0 + 51b + -51b
14 + -51b + 7b2 = 51b + -51b

Combine like terms: 51b + -51b = 0
14 + -51b + 7b2 = 0

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

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

Simplifying
2 + -7b = 0

Solving
2 + -7b = 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 + -7b = 0 + -2

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

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

Divide each side by '-7'.
b = 0.2857142857

Simplifying
b = 0.2857142857
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 = {0.2857142857, 7}