What is x if 2x-3/x=11?

Oct 28, 2015

$x = \frac{11 + \sqrt{145}}{4} , \frac{11 - \sqrt{145}}{4}$

Explanation:

$2 x - \frac{3}{x} = 11$

Multiply both sides by the LCD $x$.

$2 x \left(x\right) - \frac{3}{\cancel{x}} \left(\cancel{x}\right) = 11 \left(x\right) =$

$2 {x}^{2} - 3 = 11 x$

Move all terms to the left side.

$2 {x}^{2} - 3 - 11 x = 0$

Rearrange the terms.

$2 {x}^{2} - 11 x - 3$

$2 {x}^{2} - 11 x - 3$ is in the form of a quadratic equation $a x + b x + c$, where $a = 2 , b = - 11 , \mathmr{and} c = - 3$.

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a} =$

$x = \frac{- \left(- 11\right) \pm \sqrt{\left(- {11}^{2}\right) - \left(4 \cdot 2 \cdot - 3\right)}}{2 \cdot 2} =$

$x = \frac{11 \pm \sqrt{121 + 24}}{4} =$

$x = \frac{11 \pm \sqrt{145}}{4}$

Solve for $x$.

$x = \frac{11 + \sqrt{145}}{4} , \frac{11 - \sqrt{145}}{4}$