Let's see:

x + sqrt(x-1) = 2x – 7
sqrt(x-1) = x – 7
(x-1) = x^2 -14x +49
x^2 – 15x + 50 = 0
(x-10)(x-5) =0
x = 5 or 10

x =5 doesn't work since you get 7 = 3, which is false. If you do x = 10, it would give you 13 =13, which is true.

So overall, X = 10, which is Lyra's score.

Dat algebra.