S = 6ab + 4a^3

Make b the subject of the formula

Solve for b:S = 4 a^3 + 6 a b

S = 4 a^3 + 6 a b is equivalent to 4 a^3 + 6 a b = S:4 a^3 + 6 a b = S

Subtract 4 a^3 from both sides:6 a b = S - 4 a^3

Divide both sides by 6 a:Answer: b = S / (6 a) - (2 a^2) / 3