Question

Solve the following equation using the formula: 

`4/x - 3 = 5/(2x + 3)` 

Answer 1

`4/x - 3 = 5/(2x + 3)`  

`\implies (4-3x)/x=5/(2x+3)` 

`\implies` (4 – 3x)(2x + 3) = 5x 

`\implies` 8x + 12 – 6x² – 9x = 5x 

`\implies` 6x² + 6x – 12 = 0

`\implies`  x² + x – 2 = 0

Here a = 1, b = 1 and c = –2 

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

= `(-(1) +- sqrt((1)^2 - 4(1)(-2)))/(2(1)` 

= `(1 +- sqrt(9))/2`

= `(-1 +- 3)/2`

= `(-1 + 3)/2` and `(-1 - 3)/2`

= 1 and –2