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Question
Solve the following equation by using formula :
`x(3x + 1/2)` = 6
Solution
`x(3x + 1/2)` = 6
`3x^2 + x/(2)` = 6
⇒ 6x2 + x = 12
⇒ 6x2 + x – 12 = 0
Here a = 6, b = 1, c = –12
D = b2 – 4ac
= (1)2 – 4 x 6 x (–12)
= 1 + 288
= 289
∵ x = `(-b ± sqrt("D"))/(2a)`
= `(-1 ± sqrt(289))/(2 xx 6)`
= `(-1 ±17)/(12)`
∴ x1 = `(-1 + 17)/(12)`
= `(16)/(12)`
= `(4)/(3)`
x2 = `(-1 - 17)/(12)`
= `(-18)/(12)`
= `-(3)/(2)`
∴ x = `(4)/(3), (3)/(2)`.
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