Thrice the square of a natural number decreased by 4 times the number is equal to 50 more than the number. The number is :

Question: Thrice the square of a natural number decreased by 4 times the number is equal to 50 more than the number. The number is :

Solution:
Let the number be x

Then,
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 = 5

Hence, the number is 5