Question

Solve the following equation by using formula :

10ax² – 6x + 15ax – 9 = 0,a≠0

Answer 1

10ax² – 6x + 15ax – 9 = 0
Here a = 10a, b = –(6 - 15a), c = –9
D = b² – 4ac
= [–(6 – 15a)]² – 4 x 10a(–9)
= 36 – 180a + 225a² + 360a
= 36 + 180a + 225a² = (6 + 15a)²

∴ x = `(-b ± sqrt("D"))/(2a)`

= `(-[-(6 - 15a)] ± sqrt((6 + 15a)^2))/(2 xx 10a)`

= `((6 - 15a) ± (6 + 15a))/(20a)`

∴ x₁ = `(6 - 15a + 6 + 15a)/(20a)`

= `(12)/(20a)`

= `(3)/(5a)`

x₂ = `(6 - 15a - 6 - 15a)/(20a)`

= `(-30a)/(20a)`

= `(-3)/(2)`

Hence x = `(3)/5a), (-3)/(2)`.