3x2+11=0

To solve the equation \(3x^2 + 11 = 0\), we can start by isolating the \(x^2\) term:

1. Subtract 11 from both sides: \[ 3x^2 = -11 \]

2. Divide both sides by 3: \[ x^2 = -\frac{11}{3} \]

Since \(x^2\) cannot be negative in the set of real numbers, this equation has no real solutions. However, we can find complex solutions by taking the square root of both sides:

3. Taking the square root: \[ x = \pm \sqrt{-\frac{11}{3}} = \pm \sqrt{\frac{11}{3}} i \] (where \(i\) is the imaginary unit).

Thus, the solutions are: \[ x = \pm \frac{\sqrt{11}}{\sqrt{3}} i \quad \text{or} \quad x = \pm \frac{\sqrt{33}}{3} i \]