Question

$x - 3 - \frac{4}{x} = 0$

Answer 1

x - 3 - ( 4 / x ) = 0
x ≠ 0
x( x - 3 ) - 4 = 0
x^2 - 3x - 4 = 0
D = 9 + 16 = 25 = 5^2
x1 = ( 3 + 5 ) : 2 = 4 
x2 = ( 3 - 5 ) : 2 = - 1 

Answer 2

$x-3- \frac{4}{x}=0$
$\frac{x^2-3x-4}{x}=0$
$x^2-3x-4=0$
$x= \frac{3+ \sqrt{9+16} }{2}$
$x= \frac{3+ \sqrt{25} }{2}$
$x= \frac{3+5}{2}$
$x= \frac{3-5}{2}$
$x_{1}=-1$
$x_{2}=4$