# What is x if x-3/x^2+14=8?

Oct 14, 2017

$x - \frac{3}{x} ^ 2 + 14 = 8$

Subtract 8 from each side:
$x - \frac{3}{x} ^ 2 + 6 = 0$

Multiply each side by ${x}^{2}$:
$\left({x}^{2}\right) \left(x - \frac{3}{x} ^ 2 + 6\right) = 0$

Distribute and simplify:
${x}^{3} - 3 + 6 {x}^{2} = 0$

$0 = {x}^{3} + 6 {x}^{2} - 3$

From here, I think the best option to solve this would be to use a graphing calculator. On the TI-84 plus, I used the numeric solver.

$x = - .671 , x = .756 , x = 5.914$