X*17x+35=341

To solve the equation \( x \cdot 17x + 35 = 341 \), we first rewrite it in standard form.

1. Distribute and combine like terms: \[ 17x^2 + 35 = 341 \]

2. Subtract 341 from both sides to set the equation to zero: \[ 17x^2 + 35 - 341 = 0 \] \[ 17x^2 - 306 = 0 \]

3. Now, add 306 to both sides: \[ 17x^2 = 306 \]

4. Divide both sides by 17 to isolate \( x^2 \): \[ x^2 = \frac{306}{17} \] \[ x^2 = 18 \]

5. Take the square root of both sides: \[ x = \sqrt{18} \quad \text{or} \quad x = -\sqrt{18} \]

6. Simplifying \( \sqrt{18} \): \[ x = \sqrt{9 \cdot 2} = 3\sqrt{2} \quad \text{or} \quad x = -3\sqrt{2} \]

Thus, the solutions for \( x \) are: \[ x = 3\sqrt{2} \quad \text{and} \quad x = -3\sqrt{2} \]