The angry arjun carried some arrows …

Suppose Arjun had x arrows.
Number of arrows used to cut arrows of Bheeshm = x/2
Number of arrows used to kill the rath driver = 6
Number of other arrows used = 3 (required to knock down rath, flag & bow of bheem)
According to the question;  Remaining arrows = {tex}4 \sqrt { x } + 1{/tex}
Total no. of arrows Arjuna had = {tex}\quad \frac { x } { 2 } + 6 + 3 + 4 \sqrt { x } + 1{/tex}
{tex}\therefore \quad \frac { x } { 2 } + 6 + 3 + 4 \sqrt { x } + 1 = x{/tex}{tex}\Rightarrow\frac{\displaystyle x}{\displaystyle2}+10+4\sqrt x=x{/tex}
{tex}\Rightarrow \quad x + 20 + 8 \sqrt { x } = 2 x{/tex}
{tex}\Rightarrow \quad x = 20 + 8 \sqrt { x }{/tex}
Putting {tex}\sqrt x=y\Rightarrow y=x^2{/tex} , the above equation becomes
       y² = 20 + 8y
{tex}\Rightarrow{/tex} y² - 8y - 20 = 0
{tex}\Rightarrow{/tex} y² -10y +2y -20 = 0
{tex}\Rightarrow{/tex} (y - 10) (y + 2) = 0
{tex}\Rightarrow{/tex} y = 10 or. y = -2
{tex}\Rightarrow{/tex} y = 10 [{tex}\because{/tex} y cannot be negative , as it is square root of x ]
{tex}\Rightarrow{/tex} x = y² {tex}\Rightarrow{/tex} x = 100
Hence, the number of arrows which Arjun had is x = 100.