[tex] \sqrt{ - 35 + 12x = x} [/tex]

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Squaring both sides to eliminate the square root,

-35 + 12x = x^
]

Rearranging the equation to standard form,

x^2 - 12x + 35 =
]

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

Factorizing the quadratic equation,

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

Setting each factor to zero,

x-5 = 0 \implies x =
]

x-7 = 0 \implies x =
]

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