Solve the equation: x^2 + x + 3 = 0

This is a quadratic equation. To solve it, the most straightforward way is to use the quadratic formula, which is described as below.

x = \frac{-b \pm \sqrt{b^2 - 4 a c}}{2 a}

where $a$ is 1, $b$ is 1 and $c$ is 3. With all these, the solutions are:

x = \frac{-1 \pm \sqrt{1^2 - 4 \cdot 1 \cdot 3}}{2 \cdot 1} = \frac{-1 \pm \sqrt{-11}}{2} = -\frac{1}{2} \pm \frac{11}{2} i

As you can see, there is no real solution to this equation, therefore these solutions are in the complex world.