Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.

Explanation

Let, the natural number be x.
According to given condition
`x^(2)-84=3(x+8)`
`impliesx^(2)-84=3x+24impliesx^(2)=3x-108=0`
`impliesx^(2)-(12-9)x-108=0impliesx^(2)-12x+9x-108=0`
`impliesx(x-12)+9(x-12)=0implies(x-12)(x+9)=0`
`impliesx-12=0orx+9=0`
`impliesx=12orx=-9`
But-9 is not a natural number.
`because` Requird natural number=12.