Answer
$$w=\frac{-1+\sqrt{17}}{2},\:w=\frac{-1-\sqrt{17}}{2}$$
Work Step by Step
The quadratic formula states:
$$x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$
Thus, solving the equation, we find:
$$ w_{1,\:2}=\frac{-1\pm \sqrt{1^2-4\cdot \:1\left(-4\right)}}{2\cdot \:1} \\ w=\frac{-1+\sqrt{17}}{2},\:w=\frac{-1-\sqrt{17}}{2}$$