(square root of x-10) - 3x = 1

To solve the equation (square root of x-10) - 3x = 1, we need to isolate the variable x. Here's how you can do it:

1. Start by adding 3x to both sides of the equation to move all terms involving x to one side:
(square root of x-10) = 3x + 1

2. Next, square both sides of the equation to eliminate the square root:
[(square root of x-10)]^2 = (3x + 1)^2

3. Simplify the right side of the equation by expanding the square:
x - 10 = 9x^2 + 6x + 1

4. Rearrange the terms to move all terms to one side of the equation:
9x^2 + 6x + 1 - x + 10 = 0

5. Combine like terms:
9x^2 + 5x + 11 = 0

Now, you have a quadratic equation. You can solve it using various methods such as factoring, completing the square, or using the quadratic formula.