Question

Solve the following equation by using formula :

`x(3x + 1/2)` = 6

Answer 1

`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)`.