$x^{2}-9 x+18=0$

Step 1 ：This is a quadratic equation in the form of \(ax^{2}+bx+c=0\). The solutions to a quadratic equation can be found using the quadratic formula, which is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). In this case, \(a=1\), \(b=-9\), and \(c=18\).

Step 2 ：Substitute \(a=1\), \(b=-9\), and \(c=18\) into the quadratic formula.

Step 3 ：Calculate the discriminant \(D\) using the formula \(D=b^{2}-4ac\). In this case, \(D=9\).

Step 4 ：Substitute \(D=9\) into the quadratic formula to find the roots of the equation. The roots are \(x1=3.0\) and \(x2=6.0\).

Step 5 ：The solutions to the equation \(x^{2}-9 x+18=0\) are \(\boxed{3}\) and \(\boxed{6}\).