Use the quadratic formula to solve the equation. (Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.)
4x^2 - x + 3 = 0
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, we have a = 4, b = -1, and c = 3. Plugging these values into the quadratic formula, we get:
x = (-(-1) ± √((-1)^2 - 4(4)(3))) / (2(4))
Simplifying further:
x = (1 ± √(1 - 48)) / 8
x = (1 ± √(-47)) / 8
Since the discriminant (√(-47)) is negative, we have to introduce the imaginary unit i. Therefore, the solutions are:
x = (1 + √(-47)i) / 8, and x = (1 - √(-47)i) / 8