Given, Number of blue balls =5 Number of balls =x Total number of balls =5+x Total number of balls =5+x Number of ways of drawing 2 blue balls =‌5C2 Number of ways of drawing 2 balls =‌(5+x)C2 Given, P( drawing 2 blue balls )=‌
5
14
⇒‌‌‌
‌5C2
(5+x)C2
=‌
5
14
⇒‌‌‌
10
(5+x)(4+x)
2×1
=‌
5
14
⇒‌‌‌
20
x2+9x+20
=‌
5
14
⇒‌‌x2+9x+20=56 ⇒‌‌x2+9x−36=0 ⇒‌‌x2+12x−3x−36=0 ⇒‌‌x(x+12)−3(x+12)=0 ⇒‌‌x=3 ( ∵ Number of balls can not be negative.)