\[ \begin{align}
x^2 - 3x + 1 &= 0 \\
\end{align}\ \]
There are no obvious integer factors so use the quadratic formula
\[ \begin{align}
x &= \frac{3 \pm \sqrt{(-3)^2-4.1.1}}{2} \\
&= \frac{3}{2} \pm \frac{\sqrt 5}{2}
\end{align}\ \]
You will gain most benefit if you work through each problem first and then come back and check your work against the solution.
y
Now You Try:
If
\[ f(x) = 2x^2 + 3x + 5 \qquad \qquad \qquad \ \]
When is f(x) = 4?