Find the roots of the following quadratic equations by factorisation method :
(i) `2x^(2)+(5)/(3)x-2=0` (ii) `(2)/(5)x^(2)-x-(3)/(5)=0` (iii) `3sqrt2x^(2)-5x-sqrt2=0`
(iv) `3x^(2)+5sqrt5x-10=0`
(v) `21x^(2)-2x+(1)/(21)=0`

Explanation

Let's solve each of the given quadratic equations step by step using the factorization method.

### (i) \( 2x^2 + \frac{5}{3}x - 2 = 0 \)

1. **Clear the fraction by multiplying through by 3**:
\[ 3(2x^2) + 3\left(\frac{5}{3}x\right) - 3(2) = 0 \implies 6x^2 + 5x - 6 = 0 \]
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