Question

Solve the following equation by using formula :

(2x + 3)(3x – 2) + 2 = 0

Answer 1

(2x + 3)(3x – 2) + 2 = 0
6x² - 4x + 9x - 6 + 2 = 0
6x² + 5x - 4 = 0
Here a = 6, b = 5, c = -4
D = b² - 4ac
= (5)² - 4 x 6 x (-4)
= 25 + 96
= 121

∵ x = `(-b + sqrt("D"))/(2a)`

= `(-5 ± sqrt(121))/(5 xx 6)`

= `(-5 ±11)/(12)`

∴ x₁ = `(-5 + 11)/(12)`

= `(6)/(12)`

= `(1)/(2)`

∴ x₂ = `(-5 - 11)/(12)`

= `(-16)/(12)`

= `(-4)/(3)`

Hence x = `(1)/(2), (-4)/(3)`.