Let's simplify the given equation step by step to solve for b:
2(b + 5) / (6b² - 3) = 5 + 7b - 1
First, we can simplify the right-hand side by combining like terms:
2(b + 5) / (6b² - 3) = 7b + 4
Next, we can cross-multiply to get rid of the fraction:
2(b + 5) = (7b + 4)(6b² - 3)
Expand the right-hand side using the distributive property:
2(b + 5) = 42b³ + 19b - 12
Simplify the left-hand side by distributing the 2:
2b + 10 = 42b³ + 19b - 12
Move all the terms to one side of the equation:
42b³ - 2b + 19b - 12 - 10 = 0
Combine like terms:
42b³ + 17b - 22 = 0
We can solve for b using numerical methods, such as the Newton-Raphson method or the bisection method. However, there is no exact algebraic solution for b in this case.