I have ti find the two solutions to this equation. This problem deals with imaginary numbers i {3x}^(2) - x + 4 = 0​

Question

I have ti find the two solutions to this equation. This problem deals with imaginary numbers i


`{3x}^(2) - x + 4 = 0`​

Answer 1

`x = (1)/(6) + (i√(47))/(6)` or
`x = (1)/(6) - (i√(47))/(6)`

Explanation:

Use the quadratic formula.

`x = (-b \pm √(b^2 - 4ac))/(2a)`

`x = (-(-1) \pm √((-1)^2 - 4(3)(4)))/(2(3))`

`x = (1 \pm √(1 - 48))/(6)`

`x = (1 \pm √(-47))/(6)`

`x = (1)/(6) \pm (i√(47))/(6)`

`x = (1)/(6) + (i√(47))/(6)` or
`x = (1)/(6) - (i√(47))/(6)`