# How do you solve the quadratic 3+1/x=10/x^2 using any method?

Dec 7, 2016

$x = - 2$ or $+ \frac{5}{3}$

#### Explanation:

$3 + \frac{1}{x} = \frac{10}{x} ^ 2$

Multiply through by ${x}^{2} \to 3 {x}^{2} + x = 10$

$3 {x}^{2} + x - 10 = 0$

$\left(x + 2\right) \left(3 x - 5\right) = 0$

$x =$either $- 2$ or $+ \frac{5}{3}$