Question

Solve the following equation by using formula:

2x² – 6x + 3 = 0

Answer 1

2x² – 6x + 3 = 0
Here a = 2, b = -6, c = 3
then D = b² - 4ac 
= (-6)² - 4 x 2 x 3
= 36 - 24
= 12
Now 
x = `(-b ± sqrt("D"))/(2a)`

= `((-6) ± sqrt(12))/(2 xx 2)`

= `(6 ±2sqrt(3))/(4)`

∴ x₁ = `(6 + 2sqrt(3))/(4)`

= `(2(3 + sqrt(3)))/(4)`

= `(3 + sqrt(3))/(2)`

x₂ = `(6 - 2sqrt(3))/(4)`

= `(2(3 - sqrt(3)))/(4)`

= `(3 - sqrt(3))/(2)`

Hence x = `(3 + sqrt(3))/(2), (3 - sqrt(3))/(2)`.