Five times of a positive integer is less than twice its square by 3.
Find the integer.

The positive integer is 3.

Step-by-step explanation:

Let 'x' be the integer

Given that five times of a positive integer is less than twice its square by 3.

so

5 times of x =

3 less than twice of the square of x =

so the equation becomes

Factorise

Using the zero factor principle

if ab=0, then a=0 or b=0 (or both a=0 and b=0)

solving

Subtract 1 from both sides

Simplify

Divide both sides by 2

Simplify

Also solving

Add 3 to both sides

simplify

Thus, we got integers:

x = 3 or x = -1/2

Therefore, the positive integer is 3.