Find the roots of following quadratic equations by using quadratic formula, if they exist.
(i)`2x^(2)+x-4=0` (ii) `2x^(2)+x+4=0`
(iii) `2x^(2)+5sqrt3x+6=0` (iv) `sqrt3x^(2)+11x+6sqrt3=0`

Explanation

Let's solve the given quadratic equations step by step using the quadratic formula.

### Part (i): Solve \(2x^2 + x - 4 = 0\)

1. **Identify coefficients**:
- \(a = 2\), \(b = 1\), \(c = -4\)

2. **Calculate the discriminant** \(D\):
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