Find the roots of the following quadratic equation by the factorization method.
$2 x^{2} + \frac{5}{3} x - 2 = 0$

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Solution

Given equation is
$2 x^{2} + \frac{5}{3} x - 2 = 0$
$\Rightarrow 6 x^{2} + 5 x - 6 = 0$
$\Rightarrow 6 x^{2} + 9 x - 4 x - 6 = 0$
$\Rightarrow 3 x (2 x + 3) - 2 (2 x + 3) = 0$
$\Rightarrow (2 x + 3) (3 x - 2) = 0$
$\Rightarrow 2 x + 3 = 0$ or $3 x - 2 = 0$
$\Rightarrow 2 x = - 3$ or $3 x = 2$
$\Rightarrow x = \frac{- 3}{2}$ or $x = \frac{2}{3}$

So, the roots of the given quadratic equation are $\frac{- 3}{2}$ or $x \frac{2}{3}$

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