Had Aarush scored 8 more marks in a Mathematics test, out of 35 marks, 7 times these marks would have been 4 less than square of his actual marks. How many marks did he get in the test?

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Step 1: Let actual marks be $x$.
ATQ: $7(x + 8) = x^2 - 4$
Step 2: $x^2 - 7x - 60 = 0$
$x^2 - 12x + 5x - 60 = 0$
$(x - 12)(x + 5) = 0$
Step 3: $x = 12$, $x = -5$ (rejecting)
Step 4: $	herefore$ Actual marks obtained by Aarush $= 12$

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