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Question
Solve the following equation using the formula:
`4/x - 3 = 5/(2x + 3)`
Solution
`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
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