Squaring both sides to eliminate the square root,

[
-35 + 12x = x^2
]

Rearranging the equation to standard form,

[
x^2 - 12x + 35 = 0
]

Now, we need to solve this quadratic equation to find the value(s) of x.

Factorizing the quadratic equation,

[
(x-5)(x-7) = 0
]

Setting each factor to zero,

[
x-5 = 0 \implies x = 5
]

[
x-7 = 0 \implies x = 7
]

Therefore, the solutions to the equation are x = 5 and x = 7.