## Elementary Algebra

Step 1: Comparing $x^{2}-2x+6=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$, we obtain: $a=1$, $b=-2$ and $c=6$ Step 2: The quadratic formula is: $x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Step 3: Substituting the values of a, b and c in the formula: $x=\frac{-(-2) \pm \sqrt {(-2)^{2}-4(1)(6)}}{2(1)}$ Step 4: $x=\frac{2\pm \sqrt {4-24}}{2}$ Step 5: $x=\frac{2 \pm \sqrt {-20}}{2}$ Since their are no real number solutions to $\sqrt {-20}$, there are no real number solutions to the equation.