# How do you solve  3/(5(x-2)) = x-4?

Jul 23, 2016

$x = 4.265 \text{ or } x = 1.735$

#### Explanation:

Write the equation as $\frac{3}{5 \left(x - 2\right)} = \frac{x - 4}{1}$

There is now one fraction term on each side and we can cross-multiply. We would have had the same result if we had multiplied both sides by the denominator.

$5 \left(x - 2\right) \left(x - 4\right) = 3$

$5 \left({x}^{2} - 4 x - 2 x + 8\right) - 3 = 0 \text{ make a quadratic =0}$

$5 {x}^{2} - 20 x - 10 x + 40 - 3 = 0$

$5 {x}^{2} - 30 x + 37 = 0$

THere are no factors of 5 and 37 which will make 30, we need to use the formula: $a = 5 , b = - 30 c = 37$

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

$x = \frac{- \left(- 30\right) \pm \sqrt{{\left(- 30\right)}^{2} - 4 \left(5\right) \left(37\right)}}{2 \left(5\right)}$

$x = \frac{30 \pm \sqrt{900 - 740}}{10}$

$x = \frac{30 + \sqrt{160}}{10} \text{ or } x = \frac{30 - \sqrt{160}}{10}$

$x = 4.265 \text{ or } x = 1.735$