The number is such that when its square is multiplied by three and then reduced by four times the number, the result is fifty greater than the number itself. What is the number?

Question: The number is such that when its square is multiplied by three and then reduced by four times the number, the result is fifty greater than the number itself. What is the number?Solution:Let the number be xThen,3x2 - 4x = x + 50⇒ 3x2 - 4x - x - 50 = 0⇒ 3x2 - 5x - 50 = 0⇒ 3x2 - 15x + 10x - 50 = 0⇒ 3x(x - 5) + 10(x - 5) = 0⇒ (x - 5)(3x + 10) = 0∴ x = 5Hence, the number is 5