Had Ajita scored 10 more marks in her mathematics . . .

Question : Had Ajita scored 10 more marks in her mathematics test out of 30 marks, 9 times these marks would have been the square of her actual marks. How many marks did she get in the test?

Doubt by Zoha 

Solution : 

Let the actual marks scored by Ajita in her test be x.

ATQ

9(x+10)=x²

9x+90=x²

0=x²-9x-90
x²-9x-90=0
Factorising by Splitting the Middle Terms

x²-(15-6)x-90=0
x²-15x+6x-90=0
x(x-15)+6(x-15)=0
(x+6)(x-15)=0

x+6=0 
x=-6

but marks can't be -ve.
Rejected

OR

x-15=0
x=15

Hence, the actual marks scored by Ajita in the test is 15.