The standard form of a quadratic equation is expressed as
ax^2 + bx + c = 0
The given equation is
x^2 - 3x + 1 = 0
By comparing the equation with the standard equation, we have
a = 1, b = - 3, c = 1
The quadratic formula is expressed as
[tex]\begin{gathered} x\text{ = }\frac{-\text{ b}\pm\sqrt[]{b^2-4ac}}{2a} \\ \text{Substituting the given values into the formula, } \\ x\text{ = }\frac{-\text{ - 3}\pm\sqrt[]{-3^2-4(1\times1)}}{2\times1} \\ x\text{ = }\frac{3\pm\sqrt[]{9\text{ - 4}}}{2}\text{ or }\frac{3\pm\sqrt[]{5}}{2} \end{gathered}[/tex][tex]x\text{ = }\frac{3+\sqrt[]{5}}{2}\text{ or x = }\frac{3-\sqrt[]{5}}{2}[/tex]