Solve x(x-1/2)=65/18

$$x ( x - \frac { 1 } { 2 } ) = \frac { 65 } { 18 }$$

Evaluate

$$\frac{65}{18}\approx 3.611111111$$

Steps For Long Division Method

Use the 1^{st} digit 6 from dividend 65

$$\begin{array}{l}\phantom{18)}\phantom{1}\\18\overline{)65}\\\end{array}$$

Since 6 is less than 18, use the next digit 5 from dividend 65 and add 0 to the quotient

$$\begin{array}{l}\phantom{18)}0\phantom{2}\\18\overline{)65}\\\end{array}$$

Use the 2^{nd} digit 5 from dividend 65

$$\begin{array}{l}\phantom{18)}0\phantom{3}\\18\overline{)65}\\\end{array}$$

Find closest multiple of 18 to 65. We see that 3 \times 18 = 54 is the nearest. Now subtract 54 from 65 to get reminder 11. Add 3 to quotient.

$$\begin{array}{l}\phantom{18)}03\phantom{4}\\18\overline{)65}\\\phantom{18)}\underline{\phantom{}54\phantom{}}\\\phantom{18)}11\\\end{array}$$

Since 11 is less than 18, stop the division. The reminder is 11. The topmost line 03 is the quotient. Remove all zeros at the start of the quotient to get the actual quotient 3.

$$\text{Quotient: }3 \text{Reminder: }11$$

Factor

$$\frac{5 \cdot 13}{2 \cdot 3 ^ {2}} = 3\frac{11}{18} = 3.611111111111111$$