Answer:
x=-4.37 or 1.37
Step-by-step explanation:
The equation whose solution is to be found is;
[tex]1 + \frac{3}{x}= \frac{6}{ {x}^{2} } [/tex]
we now multiply through by
[tex]{x}^{2} [/tex]
This implies that;
[tex]( {x}^{2})1 +({x}^{2} \times \frac{3}{x})= {x}^{2} \times \frac{6}{ {x}^{2} }[/tex]
[tex] \implies{x}^{2}+3x=6[/tex]
Subtracting - 6 from both side we obtain;
[tex] {x}^{2} + 3x - 6 = 6 - 6[/tex]
[tex] \implies{x}^{2} + 3x - 6 =0[/tex]We now obtain a quadratic equation.So, let us use quadratic formula to find the solutions.
Comparing the equation ,
[tex]{x}^{2} + 3x - 6 = 0[/tex]
to the general quadratic formula,
[tex]a {x}^{2} + bx + c = 0[/tex]
we can say that,
a=1,b=3 and c=-6
putting this in to the quadratic formula,
[tex] \implies x = \frac{ -b\pm \sqrt{{b}^{2} - 4ac} }{2a} [/tex], we obtain
[tex]x = \frac{-3\pm \sqrt{ {3}^{2} - 4(1)(-6)} }{2(1)} [/tex]
Simplifying we obtain,
[tex] x = \frac{ -3\pm \sqrt{9+24}}{2} [/tex]
[tex] \implies x = \frac{-3-\sqrt{33} }{2}or \frac{-3+\sqrt{33}}{2} [/tex]
x=-4.37 or 1.37
