How do you solve the rational equation x+3/(2x) = 5/8?

Dec 23, 2015

Simplify then use the quadratic formula

Explanation:

Get rid of all the denominators and then solve as a standard quadratic.
$\frac{x \cdot \left(2 x\right) + 3}{2 x} = \frac{5}{8}$
$8 \left(2 {x}^{2} + 3\right) = 5 \cdot \left(2 x\right)$
$16 {x}^{2} + 24 - 10 x = 0$
Then use the quadratic formula to solve as this does not have simple factors.
$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$
$x = \frac{- 24 \pm \sqrt{{24}^{2} - 4 \cdot 16 \cdot \left(- 10\right)}}{2 \cdot 16} = \frac{- 24 \pm \sqrt{576 + 640}}{32}$
$x \approx . 0.34 \mathmr{and} - 1.84$