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

Let the number be x

Given, 5 times the number = 3 less than twice the square of the number

$\Rightarrow 5x = 2x^2 - 3 \\[0.5em] \Rightarrow 5x - 2x^2 + 3 = 0 \\[0.5em] \Rightarrow 2x^2 - 5x - 3 = 0 \text{ (on multiplying the equation by -1) } \\[0.5em] \Rightarrow 2x^2 - 6x + x - 3 = 0 \\[0.5em] \Rightarrow 2x(x - 3) + 1(x - 3) = 0 \\[0.5em] \Rightarrow (2x + 1)(x - 3) = 0 \text{ (Factorising left side) } \\[0.5em] \Rightarrow 2x + 1 = 0 \text{ or } x - 3 = 0 \text{ (Zero-product rule) } \\[0.5em] \Rightarrow x = -\dfrac{1}{2} \text{ or } x = 3 \\[0.5em]$

Since the number is a whole number x ≠ $-\dfrac{1}{2}$

∴ x = 3

Hence, the required whole number is 3.