Question

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

Answer 1

`x = 4.265 " or "x = 1.735`

Explanation:

Write the equation as `3/(5(x-2)) = (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(x-2)(x-4) = 3`

`5(x^2-4x-2x+8)-3=0" make a quadratic =0"`

`5x^2-20x -10x+40-3=0`

`5x^2-30x+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 = (-b +-sqrt(b^2-4ac))/(2a)`

`x = (-(-30) +-sqrt((-30)^2-4(5)(37)))/(2(5))`

`x = (30+-sqrt(900-740))/10`

`x = (30+sqrt160)/10" or "x = (30-sqrt160)/10`

`x = 4.265 " or "x = 1.735`