This question has been taken from Book:- ML aggarwal, Avichal publication, class10th, quadratic equation in one variable, chapter 5, exercise 5.5

This is an important ques and asked in paper

Five times a certain whole number is equal to three less than twice the square of the number. Find the number.

Question no. 4 , ML Aggarwal, chapter 5, exercise 5.5, quadratic equation in one variable, ICSE board,

Let us consider the number be â€˜xâ€™

So according to the question,

5x = 2x

^{2}Â â€“ 32x

^{2}Â â€“ 3 â€“ 5x = 02x

^{2}Â â€“ 5x â€“ 3 = 0Let us factorize,

2x

^{2}Â â€“ 6x + x â€“ 3 = 02x(x â€“ 3) + 1(x â€“ 3) = 0

(x â€“ 3) (2x + 1) = 0

So,

(x â€“ 3) = 0 or (2x + 1) = 0

x = 3 or 2x = -1

x = 3 or x = -1/2

âˆ´ The required number is 3 [since, -1/2 cannot be a whole number].